Question

Solve the exponential equation.
4^2x – 2 = 26

I know I use the one to one property to equate. But I am confused. Thanks!

Answer 1

do you mean

4^(2x) - 2 = 26 or

4^(2x-2) = 26 or

(4^2)x - 2 = 26

The way you typed it, it would be the last one, but I am sure that is not what you meant.

Answer 2

4^(2x-2)=26

Answer 3

then take log of both sides
log [4^(2x-2) }= log 26
(2x-2)log4 = log 26
2x-2 = log26/lo4
2x = (log26/log4 + 2)
x = (log26/log4 + 2)/2 = appr. 2.1751

check
4^(2(2.1751 - 2)
= 4^(4.35022 - 2)
= 4^2.35022
= 26
= RS