Question

For what value of x does


`4^(x)=((1)/(8))^(x + 5)`
-15
-3
3
15​

Answer 1

Write both sides as powers of 2:

`4^x=(2^2)^x=2^(2x)`

`\left(\frac18\right)^(x+5)=8^(-x-5)=(2^3)^(-x-5)=2^(-3x-15)`

Since both powers of 2 are equal, the exponents are equal:

2x = -3x - 15

5x = -15

x = -3