Question

For what value of x does 4^x =(1/8)^x+5

Answer 1

9514 1404 393

Answer:

(b) -3

Explanation:

It can work well to rewrite the equation as powers of 2.

`4^x=\left((1)/(8)\right)^(x+5)\\\\(2^2)^x=(2^(-3))^(x+5)\qquad\text{as powers of 2}\\\\2x=-3(x+5)\qquad\text{equate exponents}\\\\5x=-15\qquad\text{add $3x$}\\\\\boxed{x=-3}\qquad\text{divide by 5}`

__

Check

4^-3 = (1/8)^(-3+5) ⇒ 1/64 = (1/8)^2 . . . . true