Question

Provide the solution to the equation 8 =√(2)^(4x + 8).
Using complete sentences, explain the strategy used in solving this equation the way you did.

Answer 1

8 =√(2)^(4x + 8)
By factorizing 4x + 8, we've 4(x+2)
By the law of indices, sqrt(2^4(x+2)) = 2^(2(x+2))
So 2^(2(x+2)) = 2^3
Since bases are the same, compare power
2(x+2) = 3
x + 2 = 1.5
x = -0.5