# Logarithm Rules

### Definition of Logarithm

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

The logarithm with a negative base does not exist.

The logarithm of a negative number does not exist.

The logarithm of zero does not exist.

The logarithm of 1 is zero.

The logarithm with base * a* and the number

*is one.*

**a**The logarithm with base * a* of a power in base

**a**is equal to the exponent.

## Logarithm Rules

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

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

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

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

5Change of base.

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