# Inverse Operations

The inverse of an operation is the operation which gets you back to the number you started with.

For example, if you start with the number $6$ , and then add $4$ :

$6+4=10$

To get back to the $6$ , you have to subtract $4$ from $10$ .

$10-4=6$

Therefore
**
addition and subtraction
**
are
**
inverse
operations
**
.

Similarly,
**
division
**
is the inverse of
**
multiplication
**
,
and vice versa:

$\begin{array}{l}7\times 5=35\\ 35\xf75=7\end{array}$

The case of exponents and logarithms is slightly more complicated, since neither operation is commutative . After raising a number to a power, you can use the logarithm to get back to the exponent (not the base.)

${10}^{3}=1000$

${\mathrm{log}}_{3}1000\ne 10$ , but

${\mathrm{log}}_{10}1000=3$