### Logarithms

$$N={a}^{x}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\iff \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{log}}_{a}N=x$$
${\mathrm{log}}_{a}N=x$
is called the logarithmic form and
$N={a}^{x}$
is the index or exponential form.

**Note**:

- The logarithm of a negative number is not defined.
- log in the calculator denotes ${\mathrm{log}}_{10}$ or common logarithm.
- ${\mathrm{log}}_{10}$ may be written as lg.
- If the base is other than 10, the base should be specified, e.g. ${\mathrm{log}}_{3}81$