Log Calculator

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). 

log_bc =b^ca

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.

log_b(CD) = log_b(C) + log_b(D)

Quotient Rule

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

log_b(C/D) = log_bC - log_bD

Power Rule

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

log_b(x^y) = y * log_b(x)

Log base switch Rule

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

log_b(x) =1 / log_x(b)

Change of base Rule

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

 log_b(x) = log_c(x) / log_c(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