Definition of Logs

A logarithm (or log) is the inverse operation of exponentiation. Specifically, the logarithm of a number $x$ with base $b$ is the power $y$ to which the base $b$ must be raised to produce $x$ . This is written as :

\log_b(x) = y \quad \iff \quad b^y = x,

Where $b>0,b \ne1$ and $x>0$ .

infoNote

The symbol $\iff$ means "if and only if ", meaning we can replace the entire equation of the left with the equation on the right (and vice versa.)

Consider the equation :

2^x=8

We can solve this using logarithms :

\log_2(8)=x \\ x=3

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