Concept preview

What you will be able to do

1. 01Interpret a logarithm as the inverse of an exponential and convert between forms
2. 02Evaluate logarithms and use the basic identities
3. 03Solve exponential and logarithmic equations using the definition

A logarithm is the inverse of an exponential — it answers the question 'to what power must I raise the base to get this number?' Formally, $$\log_b y = x$$ means exactly $$b^{x} = y$$ (with base $b > 0$, $b \ne 1$, and $y > 0$). So $\log_2 8 = 3$ because $2^{3} = 8$. Every logarithm statement is just an exponential statement wearing different clothes, and switching between the two forms is the key skill.