Question

How do you solve `4^(2x+3) = 1`?

Answer 1

Convert to logarithmic form.

Explanation:

`log(4^(2x + 3)) = 1`

Simplify using the rule `logn^a = alogn`

`(2x + 3)log4 = 1`

You can now distribute. Don't forget: you can't combine logarithmic and non logarithmic expressions.

`2xlog4 + 3log4 = 1`

`2xlog4 = 1 - 3log4`

Factor out the x.

`x(2log4) = 1 - log4^3`

`x = (1 - log64)/log16`

Ask your teacher exactly what he/she wants. They may want you to keep your answer in exact form, or for you to round it off to a certain number of decimals, so just make sure to communicate.

Practice exercises:

1. Solve for x.

a) `2^(3x - 7) = 5`

b). `3^(2x + 3) = 4^(x - 5)`

c) `2^(4x - 9) = 3 xx 3^(x + 6)`

Good luck!