 # Log Calculator

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

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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

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