Logarithm Rules

Definition of Logarithm

Logarithm Definition

From the definition of a logarithm, it can be concluded:

The logarithm with a negative base does not exist.

Negative Base

The logarithm of a negative number does not exist.

Negative Number

The logarithm of zero does not exist.

Logarithem Zero

The logarithm of 1 is zero.

Logarithm of One

The logarithm with base a and the number a is one.

Logarithm with Base A

The logarithm with base a of a power in base a is equal to the exponent.

Power of Logarithm

Logarithm Rules

1The logarithm of a product equals the sum of the logarithms of the factors.

Logarithm Product Rule

Logarithm Product Rule

2The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.

Logarithm Quotient Rule

Logarithm Quotient Rule

3The logarithm of a power is the product of the exponent of the number and the logarithm.

Logarithm Power Rule

Logarithm Power Rule

4The logarithm of a root is equal to the quotient between the logarithm of the radicand and the index of the root.

Logarithm Root Rule

Logarithm Root Rule

5Change of base.

Logarithm Change of Base Rule

Logarithm Change of Base Rule