Question

8^(X+2)=(1/64)^(X)

Answer 1

8^(x+2) = (1/64)^x
log2(8^(x+2)) = log2((1/64)^x)
(x+2) log2(8) = (x) log2(1/64)

(x+2) 3 = x (log2(1) - log2(64))
3x +6 = x(0 - 6)

3x +6 = -6x

3x +6x = -6

9x = -6

x = (-6/9) = (-2/3)

double check:

8^((-2/3)+2)=(1/64)^(-2/3)

8^(4/3) = 64^(2/3)

3root(8^4) = 3root(64^2)

8^4 = 64^2

4096 = 4096 (good)

x = (-2/3)