Definition of logarithm. Decimal and natural logarithm (lg, ln)

Definition of logarithm

If $a>0$ , $a\neq1$ , $b>0$ , the logarithm of $b$ to base $a$ is the number $c$ such that $a^c=b$ . Write: $c=\log_a b$ (“log base $a$ of $b$ equals $c$ ”). Uniqueness: for fixed $a,b$ , $c$ is unique (because $a^x$ is strictly monotone on $\mathbb{R}$ for $a>0$ , $a\neq1$ ). Domain of the symbol $\log_a b$ in $b$ : only $b>0$ . Base $a$ : only $a>0$ and $a\neq1$ .

Read

\log_a b=c

as the inverse question to

a^c=b

Content is available with subscription.

Get full access to all courses on the platform for one year with a single payment.

Unlike other platforms that charge per course, here you get everything for one price, and after one year of use there will be no automatic charge for the following year.