top

Log Calculator

Find the value of the log by entering the base and log value in the log base calculator.

Give Us Feedback

This logarithmic calculator can compute the value of the log for any base within a matter of seconds. Through this log calculator, users can find long for any base including 10, e (ln), and 2. 

What is log?

The concept of the log is related to exponents to a great extent. According to Khan Academy:

Logarithms are another way of thinking about exponents.”

A logarithm is used to find the number which, if raised as a power to the base of the log, will calculate a certain value (log value). 

logbc =bca

Did you know?  The shell of the nautilus is a perfect example of a logarithmic spiral. Logs can be reversed with anitlog. You can use antilog calculator to find the antilog of a given value.

Log Rules

There are certain rules of log that make calculations easy. 

Product rule

If two values to be multiplied have the same log base, the answer will be equal to the sum of the individual log.

logb(CD) = logb(C) + logb(D)

Quotient Rule

Similarly, two values in the division with the same log base will be equal to the difference of the individual log. 

logb(C/D) = logbC - logbD

Power Rule

If the value of the log is raised to some power then that power will be multiplied with the log of value.

logb(xy) = y * logb(x)

Log base switch Rule

The base can be replaced with log value in a reciprocal of log equation.                              

logb(x) =1 / logx(b)

Change of base Rule

To introduce a new base in the log equation following changes are made.

 logb(x) = logc(x) / logc(b)

Daily life use of log

Some examples of the use of logarithm in daily life are:

  • Sound energy (calculating decibels
  • pH of Chemicals
  • Environmental sciences 

Log

Value

Log 0

Undefined

Log of 3

0.47712

Log of 3 base 4

0.7924

Log of 3 base 27

0.3333

Log of 3 base 2

1.5849

Log of 3/5

-0.2218

Log of 3 base 5

0.6826

Log of 2

0.3010

Log of 2 base 8

0.3333

Log of 2 base 4

0.5

Log of 2 to the base 10

0.3010

Log of 100

2

Log of 1/2

-0.3010

Log of 1 million

6

Log of 1.5

0.1760

Log 2(3)

0.9030

Value of log 5

0.6989

Log of e

0.4342

Log of infinity

Log base 2 of 8

0.3333

Log2(128)

7

Log2(105)

6.7142

Log2(100)

6.6438

Math Tools

X