# 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:

$\begin{array}{l}7×5=35\\ 35÷5=7\end{array}$

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

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