Theorems About Logarithms

In an equation y = a^x is said to be the index or exponential form and x = log_ay is said to be in the logarithmic form.

The relationship between the two forms is illustrated below:

The base of the logarithm can be changed. For example, if I would like to change the base of log_ab , which is a to a base of c, we can use the formula below :

logab = ^logcb/log_ca

The logarithm of a given number N, expressed by log N, is the correspondient exponent to the power of 10 that equals the given number. For example:

                log 1 = 0 because 10⁰ = 1
                log 100 = 2 because 10² = 100
                log 0.001 = -3 because 10^-3 = 0.001

The theorems are the following:

• log P x Q = log P + log Q

• log ^P/_Q = log P - log Q

• log (Pⁿ) = n log P

• log ⁿÖP = ¹/_n log P