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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:

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

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.)

${10}^3=1000$

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

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