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