Log Table 1 To 10
Contents
 1 What are the values of log 1 to 10?
 2 What is 2.303 in log?
 3 What is the value of log 2 to log 10?
 4 Do all logs have base 10?
 5 Is log base 10 just log?
 6 What is log 1 to the base 2?
 7 How to calculate logarithm?
 8 Can log be less than 0?
 9 What is log e in math?
 10 Is natural log base 10?
 11 What are the values of log 2 to log 10?
 12 What is the value of log 0001 to the base 10?
 13 What is the value of root 1 to 10?
 14 What is the value of log 0.1 to the base 10?
What are the values of log 1 to 10?
Log Values from 1 to 10
Log 1  

Log 2  0.3010 
Log 3  0.4771 
Log 4  0.6020 
Log 5  0.6989 
How do you find log to base 10 in a log table?
Sample Examples –
 Here the sample example to find the value of the logarithmic function using the logarithm table is given.
 Example 1:
 Find the value of log 10 2.872
 Solution:
 Step 1: Characteristic Part= 2 and mantissa part= 872
Step 2: Check the row number 28 and column number 7. So the value obtained is 4579. Step 3: Check the mean difference value for row number 28 and mean difference in column 2. The value corresponding to the row and column is 3 Step 4: Add the values obtained in step 2 and 3, we get 4582.
 Example 2:
 Find the value of log 10 (∛2.134)
 Solution:
 We know by the property of logarithms,
 log a b n = n log a b
Thus, log 10 (∛2.134) = 1/3 log 10 2.134 Now we calculate log 10 2.134 For the mantissa, check row 21 and column 3 in the logarithm table, which is 3284. Now check the mean difference 4 of the same row, which is 8. ∴ Mantissa is 3284 + 8 = 3292 For the characteristic part, since there is only 1 digit in the left side of decimal, hence characteristic is 0 ∴ log 10 2.134 = 0.3292 Then, log 10 (∛2.134) = 1/3 log 10 2.134 = 1/3 × 0.3292 = 0.10973.
What is the value of log 0 to log 10?
Value of Log of 0, and its Calculation to the Base 10 The value of log of 0 to the base 10 is undefined. This is because the logarithm is undefined for any number x such that x
Is log 1 always 0?
Log 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1. Therefore, ln 1 = 0 also.
What is 2.303 in log?
The value of log 10 base e is equal to 2.303.
Why is log 10 equal to 1?
Comparing log 10 10 with the definition, we have the base, a=10 and 10 x =b, Therefore, the value of log 10 is as follows, We know that log a a=1. Hence, the value of log 10 base 10 =1, this is because of the value of e 1 =1.
What is log10 equal to?
The value of the log can be either with base 10 or with base e. The log 10 10 value is 1 while the value of log e 10 or ln(10) is 2.302585.
Is log10 10 1 correct?
Explanation: (a) Since log a a = 1, so log 10 10 = 1.
What is the value of log 2 to log 10?
The value of log 2, to the base 10, is 0.301.
Do all logs have base 10?
Introduction to Natural and Common Logarithms
 Introduction to Natural and Common Logarithms
 Learning Objective(s)
 · Use a calculator to find logarithms or powers of base e,
 · Graph exponential and logarithmic functions of base e,
 · Find logarithms to bases other than e or 10 by using the change of base formula.
In both exponential functions and logarithms, any number can be the base. However, there are two bases that are used so frequently that mathematicians have special names for their logarithms, and scientific and graphing calculators include keys specifically for them! These are the common and natural logarithms.
 A is any logarithm with base 10.
 Recall that our number system is base 10; there are ten digits from 09, and place value is determined by groups of ten.
 You can remember a “common logarithm,” then, as any logarithm whose base is our “common” base, 10.
 Are different than common logarithms.
 While the base of a common logarithm is 10, the base of a natural logarithm is the special number,
Although this looks like a variable, it represents a fixed irrational number approximately equal to 2.718281828459. (Like pi, it continues without a repeating pattern in its digits.) e is sometimes called Euler′s number or Napier’s constant, and the letter e was chosen to honor the mathematician Leonhard Euler (pronounced oiler )., where A is the amount of money after t years, P is the principal or initial investment, r is the annual interest rate (expressed as a decimal, not a percent), m is the number of compounding periods in a year, and t is the number of years. Imagine what happens when the compounding happens frequently.
 If interest is compounded annually, then m = 1.
 If compounded monthly, then m = 12.
 Compounding daily would be represented by m = 365; hourly would be represented by m = 8,760.
 You can see that as the frequency of the compounding periods increases, the value of m increases quickly.
 Imagine the value of m if interest were compounded each minute or each second ! You can even go more frequently than each second, and eventually get compounding continuously.
Look at the values in this table, which looks a lot like the expression multiplied by P in the above formula. As x gets greater, the expression more closely resembles continuous compounding.
x  
1  2 
10  2.59374 
100  2.70481 
1000  2.71692 
10,000  2.71814 
100,000  2.71826 
1,000,000  2.71828 
Notice that although x is increasing a lot (multiplying by 10 each time!), the value of is not increasing wildly. In fact, it is getting closer and closer to 2.718281828459or the value now called e, The function f ( x ) = e x has many applications in economics, business, and biology.
 E is an important number for this reason.
 Working with Bases of e and 10 Scientific and graphing calculators all have keys that help you work with e,
 Look on your calculator and find one labeled ” e” or “exp.” (Some graphing calculators may require you to use a menu to find e,
 If you can’t see the key, consult your manual or ask your instructor.) How to evaluate exponential expressions using e (such as e 3 ) depends on your calculator.
On some calculators you press the key first then enter the exponent and press enter. On others you enter the exponent first then press the key. It is important that you know how your calculator works. With your calculator, try finding e 3, The result should be 20.0855369 (the number of digits displayed will also depend on your calculator).
Example  
Problem  Find e 1.5 using a calculator. Round your answer to the nearest hundredth.  
Enter the keystrokes needed for your calculator. If you are having trouble getting the correct answer, consult your manual or instructor.  
4.4816890  Calculator result. Then round the answer to the nearest hundredth.  
Answer  4.48  To see this worked out on a calculator, see the Worked Examples for this topic. 
You can find powers of 10 (the common base ) in the same way. Some calculators have a or key that you can use to find powers of 10. Another way to find powers of 10 is to use the or the key that will work with any base (although if you use this method, you will have to key in two numbers—the base, 10, and whatever exponent you are raising it to).
Example  
Problem  Find 10 1.5, using a calculator. Round your answer to the nearest hundredth.  
Enter the keystrokes needed for your calculator. If you are having trouble getting the correct answer, consult your manual or instructor.  
31.6227766  Calculator result. Then round the answer to the nearest hundredth.  
Answer  31.62  To see this worked out on a calculator, see the Worked Examples for this topic. 
Natural logarithms (using e as the base) and common logarithms (using 10 as the base) are also available on scientific and graphing calculators. When a logarithm is written without a base, you should assume the base is 10. For example:
 log 100 = log 10 100 = 2
 Natural logarithms also have their own symbol: ln.
 ln 100 = log e 100 = 4.60517
The logarithm keys are often easier to find, but they may work differently from one calculator to the next. Most handheld scientific calculators require you to provide the input first, then press the (common) or (natural) key. Other calculators work in reverse: press the or key, and then provide the input and press or,
Example  
Problem  Find ln 3, using a calculator. Round your answer to the nearest hundredth.  
Remember ln means “natural logarithm,” or log e, Enter the keystrokes needed for your calculator. If you are having trouble getting the correct answer, consult your manual or instructor.  
1.098612  Calculator result. Then round the answer to the nearest hundredth.  
Answer  1.10  To see this worked out on a calculator, see the Worked Examples for this topic. 
table>
Example Problem Find log 34, using a calculator. Round your answer to the nearest hundredth. Remember, when no base is specified, this is the common logarithm (base 10). Enter the keystrokes needed for your calculator. If you are having trouble getting the correct answer, consult your manual or instructor. 1.5314789 Calculator result. Then round the answer to the nearest hundredth. Answer 1.53 To see this worked out on a calculator, see the Worked Examples for this topic.table>
 Use a calculator to find ln 7.
 A) 0.845098
 B) 1.945910
 C) 1096.633
 D) 10,000,000
A) 0.845098 Incorrect. You found the value of log 7, that is, log 10 7. The correct answer is 1.945910. B) 1.945910 Correct. You correctly identified the keys on your calculator and found the natural log of 7. C) 1096.633 Incorrect. You found the value of e 7, The correct answer is 1.945910. D) 10,000,000 Incorrect. You found the value of 10 7, The correct answer is 1.945910.
Graphing Exponential and Logarithmic Functions of Base e Graphing functions with the base e is no different than graphing other exponential and logarithmic functions: Create a table of values, plot the points, and connect them with a smooth curve. You will want to use a calculator when creating the table.
Example  
Problem  Graph f ( x ) = e x,  

/td>
Start with a table of values. Don’t forget to choose positive and negative values for x, Use a calculator to find the f ( x ) values.( x, y ) pairs 
(−2, 0.1353) 
(−1, 0.3678) 
(0, 1) 
(1, 2.7182) 
(2, 7.3890) 
/td>
If you think of f ( x ) as y, each row forms an ordered pair that you can plot on a coordinate grid. Plot the points. Answer Connect the points as best you can, using a smooth curve (not a series of straight lines). Use the shape of an exponential graph to help you: the graph gets close to the x axis on the left, and gets steeper and steeper on the right.The same process works for logarithmic functions. Choose x values and use a calculator to find the y values.
Example  
Problem  Graph f ( x ) = ln x,  

/td>
Start with a table of values. If you choose x values, remember that x must be greater than 0. Choose values greater than and less than the base. The base and 1 are also good choices for x values.( x, y ) pairs 
(0.1, −2.30) 
(0.5, −0.69) 
(1, 0) 
( e, 1) 
(5, 1.60) 
(10, 2.30) 
/td>
If you think of f ( x ) as y, each row forms an ordered pair that you can plot on a coordinate grid. Plot the points. Answer Connect the points as best you can, using a smooth curve (not a series of straight lines). Use the shape of a logarithmic graph to help you: the graph gets close to the y axis for x near 0.Sometimes the inputs to the logarithm, or the exponent on the base, will be more complicated than just a single variable. In those cases, be sure to use the correct input on the calculator. Note: If your calculator uses the “input last” method for logarithms, either calculate the input separately and write it down, or use parentheses to be sure the correct input is used.
Example  
Problem  Graph f ( x ) = ln 4 x,  

/td>
Create a table of values. Although everything could be done using the calculator, let’s include a column for the input of the logarithm. This helps you avoid calculator errors. Use the table pairs to plot points. You may want to choose additional values for the table to give a better idea for the entire visible graph. Answer Connect the points as best you can, using a smooth curve,table>
Which of the following is a graph for f ( x ) = e 0.5 x ? A) B)
 C) D)
A) Incorrect. This is a linear graph. It’s actually f ( x ) = ( e 0.5 ) x, The correct answer is Graph C. B) Incorrect. This graph is decreasing, while f ( x ) = e 0.5 x is increasing. The correct answer is Graph C. C) Correct. This graph accurately shows f ( x ) = e 0.5 x, D) Incorrect. This is a graph of f ( x ) = ln(0.5 x ). The correct answer is Graph C.
Finding Logarithms of Other Bases Now you know how to find base 10 and base e logarithms of any number. What if you wanted to calculate log 7 36? Converting to an exponential equation, you have 7 x = 36. You know 7 1 is 7, and 7 2 is 49, so you can reason that x must be between 1 and 2, probably very close to 2.
Change of Base formula 
Notice that a appears as the base in both logarithms on the right side of the formula. For example,, using a new base of 10. You could also say, or even, Of course, that last one isn’t any easier to calculate than the original expression—but using the or keys on a calculator, you can use or to find log 7 36.
Example  
Problem  Find log 7 36.  
Use the Change of Base formula. You can use common logarithms or natural logarithms. For this example, let’s use common logarithms.  
Use the calculator to evaluate the quotient.  
Answer  1.84156 
If you had used natural logarithms, you would have gotten the same answer:
Example  
Problem  Find log 3 25.9.  
Use the Change of Base formula. This time, let’s use natural logarithms.  
Evaluate the quotient.  
Answer  2.9621 
table>
 Find log 5 200.
 A) 40
 B) 0.303
 C) 3.292
 D) 2.301
A) 40 Incorrect. You found the value of 200 ÷ 5. The correct answer is 3.292. B) 0.303 Incorrect. When using the change of base formula, the log of the original base is the denominator:, The correct answer is 3.292.
 C) 3.292
 Correct.
 D) 2.301
Incorrect. You found the value of log 200. The correct answer is 3.292.
Common logarithms (base 10, written log x without a base) and natural logarithms (base e, written ln x ) are used often. Scientific and graphing calculators have keys or menu items that allow you to easily find log x and ln x, as well as 10 x and e x, Using these keys and the change of base formula, you can find logarithms in any base. : Introduction to Natural and Common Logarithms
Is log base 10 just log?
MATH REVIEW: USEFUL MATH FOR EVERYONE – SECTION 4. WHAT IS A LOGARITHM? A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2 because 10 2 = 100 This is an example of a baseten logarithm.
 We call it a base ten logarithm because ten is the number that is raised to a power.
 The base unit is the number being raised to a power.
 There are logarithms using different base units.
 If you wanted, you could use two as a base unit.
 For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight: log 2 8 = 3 because 2 3 = 8 In general, you write log followed by the base number as a subscript.
The most common logarithms are base 10 logarithms and natural logarithms; they have special notations. A base ten log is written log and a base ten logarithmic equation is usually written in the form: log a = r A natural logarithm is written ln and a natural logarithmic equation is usually written in the form: ln a = r So, when you see log by itself, it means base ten log. to Logarithms, Page 2 For more information about this site contact the Distance Education Coordinator, Copyright © 2004 by the Regents of the University of Minnesota, an equal opportunity employer and educator.
Is log infinity zero?
Calculating the Log Infinity Value –
 Now, let us make ourselves familiar with the way of finding the value of log infinity with the help of the natural log function and the common log function.
 Value of log 10 Infinity
 There are two ways of denoting the log function of infinity to the base 10: log 10 ∞ and log(∞).
According to the definition of the logarithmic function, base = a. In this case, the base is 10 = a and y = ∞. Therefore, 10 x = ∞. So, to calculate the value of log infinity to the base 10, let us consider that at 10 ∞ = ∞. As the value of the, ‘y’ approaches infinity, the value of the variable ‘x’ shall also approach infinity.
 Log e ∞ = ∞
 Or,
 ln (∞) = ∞
Therefore, both the natural logarithm and the common logarithm value of infinity have the same value, i.e. infinity (∞). NOTE: the log infinity value is equal to infinity if the base of the log is >1 because here the log is an increasing function. Whereas, if the base of the log is between 0 to 1, the log infinity value is equal to negative infinity. This is because in this case, the log is a decreasing function. Now that you know the log infinity value, by following similar methods, you can easily calculate different values of logarithmic functions and solve related problems. Try your hand on the given below questions first!
What is log 1 to the base 2?
1: Find the values of following logarithm terms. Solution: (i) log 1 base 2 = log_ 1 = 0. It is true for any base.
How to calculate logarithm?
Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b x = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8.
Why log 1 is zero?
Properties of logarithm, The logarithm of 1 is always zero. There is no matter the value of base, because any number raised to 0 equals 1.
Can log be less than 0?
Why can’t logarithms be negative? — Krista King Math  Online math help While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story. The argument of a log function can only take positive arguments.
In other words, the only numbers you can plug into a log function are positive numbers. Negative numbers, and the number 0, aren’t acceptable arguments to plug into a logarithm, but why? The reason has more to do with the base of the logarithm than with the argument of the logarithm. To understand why, we have to understand that logarithms are actually like exponents: the base of a logarithm is also the base of a power function.
When you have a power function with base 0, the result of that power function is always going to be 0. In other words, there’s no exponent you can put on 0 that won’t give you back a value of 0. Or, put a different way, 0 raised to anything is always still 0.
In the same way, 1 raised to anything is always still 1. If you raise a negative number to a positive number that’s not an integer, but instead a fraction or a decimal, you might end up with a negative number underneath a square root. And as you know, unless we’re getting into imaginary numbers, we can’t deal with a negative number underneath a square root.
So 0, 1, and every negative number presents a potential problem as the base of a power function. And if those numbers can’t reliably be the base of a power function, then they also can’t reliably be the base of a logarithm. For that reason, we only allow positive numbers other than 1 as the base of the logarithm.
Then what we know is that, if the base of our power function is positive, it doesn’t matter what exponent we put on that base (it could be a positive number, a negative number, or 0), that power function is going to come out as a positive number. So in summary, because the we only allow the log’s base to be a positive number not equal to 1, that means the argument of the logarithm can only be a positive number.
Which means that in order to protect our bases, we have to only allow positive arguments inside the logarithm:
The base of the logarithm: Can be only positive numbers not equal to 1 The argument of the logarithm: Can be only positive numbers (because of the restriction on the base) The value you get for the logarithm after plugging in the base and argument: Can be positive or negative numbers
0:00 // The argument can’t be negative0:19 // Parts of the logarithm0:30 // The argument of the logarithm can’t be negative because of how the base of the logarithm is defined0:47 // The logarithm is a power function1:36 // What kind of numbers can the base of the logarithm actually be?3:11 // How does the base of the logarithm effect the argument of the logarithm?4:32 // Summary and conclusion
: Why can’t logarithms be negative? — Krista King Math  Online math help
Can log 0 be negative?
Can A Log Be Negative? – The output of a log function (also known as the exponent) can be negative in certain cases. For example:
log 2 (0.5) = 1
We can confirm this by converting to exponential form to get:
2 1 = 1 / 2 = 0.5
However, the input (argument) and the base of a log function cannot be negative (unless we want to deal with complex numbers).
Why log e is 1?
How to calculate the value of Log e? –
 Now, let us discuss how to find the value of log e using common log function and natural log function.
 Value of Log 10 e
 The log function of e to the base 10 is denoted as “log 10 e”.
 According to the definition of the logarithmic function, it is observed that
 Base, a = 10 and 10 x = b
 Therefore, the value of log e to the base 10 as follows
Log 10 e = log 10 (2.7182818) = 0.434294482 Log 10 e = 0.434294482 Where the value of e is 2.7182818. Therefore, the value of log e to the base 10 is equal to 0.434294482 Value of log e e The natural log function of e is denoted as “log e e”. It is also known as the log function of e to the base e. The natural log of e is also represented as ln(e)
 According to the properties to the logarithmic function, The value of log e e is given as 1.
 Therefore,
 Log e e = 1 (or) ln(e)= 1
 Because the value of e 1 = e.
What is log e in math?
Log e is a constant term that gives the value of the logarithmic function log x, when the value of x is equal to e. The value of log e is approximately equal to 0.4342944819 where the base of the logarithmic function is equal to 10. So, we have log 10 e = 0.4342944819.
1.  What is Log e? 
2.  Log e Value 
3.  Finding Value of Log e Base 10 
4.  What is Ln e (Log e Base e)? 
5.  Differentiation of Log e 
6.  FAQs on Log e 
Is natural log base 10?
Conversion of Natural Logs to Base10 Logs. Some business calculators have natural logarithm functions instead of base10 logarithms. Many scientific calculators have both. Natural logarithms use the number ( e = 2.7183.) as their base instead of the number 10,
What are the values of log 2 to log 10?
The value of log 2, to the base 10, is 0.301.
What is the value of log 0001 to the base 10?
The correct Answer is: −3.
What is the value of root 1 to 10?
The values of square roots 1 to 10 between 1 and 3 are √1 (1), √2(1.414), √3(1.732), √4 (2), √5 (2.236), √6 (2.449), √7 (2.646), √8 (2.828), and √9 (3).
What is the value of log 0.1 to the base 10?
Therefore, we obtain that the value of logarithm of 0.1 to the base 10 is 1. Hence, we obtain the correct answer as 1 which is option (c).