Logarithms

Logarithms

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

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