Question

How do you solve `4^ { x - 3} = 32`?

Answer 1

`x = 11/2 = 5 1/2 = 5.5`

Explanation:

When you have a variable in the index, you are working with an exponential equation.

There are 2 types of exponential equations

• those that can be calculated by using known powers,
• and those that need to be calculated using logs and a calculator.

This example is an example of the former, because both bases are powers of 2.

`4^(x-3) = 32`

`(2^2)^(x-3) = 2^5`

`2^(2x-6) = 2^5" "larr` if the bases are equal, the indices are equal

`:. 2x-6 = 5`

`2x = 5+6`

`2x =11`

`x = 11/2 = 5 1/2 = 5.5`