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:

7 × 5 = 35

35 ÷ 5 = 7

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.)

103 = 1000

log31000 ≠ 10, but

log101000 = 3