• Home

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$10$.

$10-4=6$

Thereforeaddition and subtractionareinverse operations.

Similarly,divisionis the inverse ofmultiplication, and vice versa:

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

The case ofexponentsandlogarithmsis slightly more complicated, since neither operation iscommutative. 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

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