Question

Solve the following exponential equations.
(2x)^x = 8^x

Answer 1

x = 4

Explanation:

Dividing by 8^x, we have ...

(2x/8)^x = 1

(x/4)^x = 1

x(log(x) -log(4)) = 0 . . . . . taking logarithms

The values of x that make the factors of this product 0 are ...

x = 0 . . . . . extraneous, as 0^0 is indeterminate

log(x) = log(4) ⇒ x = 4