Logarithm Rules | Properties

This worksheet helps you to understand some of the facts, rules and properties of logarithm computation.

1. Logarithms do not exist for zero or negative numbers.
2. Numbers greater than 1 have positive logarithms; numbers less than one but greater than zero have negative logarithms.

Some Rules & Properties for Logarithm:
log(axb) = log a + log b --->Logarithm Multiplication Property
log(a/b) = log a - log b --->Logarithm Division Property
log a^n = n log a --->Logarithm for Powers Property
log _a(a)=1 --->Logarithm Property for base
log₂5=log 5/log 2 ---->Logarithm property for changing base value

Solving Logarithm Example:
Example for Changing Base
1. Find Log₂5 using Log base 10.
So to Find Log₂5 .
Log₂5 = Log 5/Log 2
Log₂5 = 0.699/0.3010
Log₂5 = 2.3222

Example for Square root:
2. Solve Log₁₀√10
Log₁₀√10=Log₁₀(10)^1/2
Log₁₀√10=1/2 x Log₁₀10
Log₁₀√10=1/2 x 1
Log₁₀√10=1/2

When you try to solve logarithm functions, this log calculator can be used to verify the results.