Question

Solve this exponential equation with the same base on both sides.
8^(1-x) = 1/4^(x+2)

Answer 1

x = 7

Explanation:

You want to solve 8^(1-x) = 1/4^(x+2) by rewriting it with the same base on both sides.

Base 2

We can substitute ...

8 = 2^3

1/4 = 2^-2

And that will give ...

(2^3)^(1-x) = (2^-2)^(x+2)

2^(3 -3x) = 2^(-2x -4)

Solution

Equating exponents, we have ...

3 -3x = -2x -4

7 = x . . . . . . . add 3x +4

The solution is x = 7.