Question

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

Answer 1

`x=-3/2`

Explanation:

Properties of logarithms
`y=log_ax` is the same as `a^y=x`

Your posted equation will be `2x+3=log_4 1`

To solve the right side, if you don't have a calculator that with a change of base: Enter `LOG(1)`/LOG(4) into your calculator to get the correct answer. You divide the log by the number you want to change the base to.

That gives you 2x+3=0. From there it's simple algebra. Subtract the 3 from each side and divide both sides by 2. Leaving you with `x=-3/2` .

Always check your answers. `4^(2*(-3/2)+3` = 1