Solve the following equations for x and check the solution using log.

Question

2^6x-1 = 28

The answer is log56/6log2. Explain each step.

Answer 1

I will assume you meant:
2^(6x-1) = 28
take log of both sides and use rules of logs

(6x-1) log2 = log28
6x-1 = log28/log2
6x = log28/log2 + 1
x = (log28/(6log2)) + 1/6 which has the same value as log56/(6log2) using my calculator

so they must have done it a different way, let's see...

2^6x-1 = 28
multiply both sides by 2
2(2^(6x-1)) = 56
2^(6x) = 56
log it
6x log2 = log56
6x = log56/log2
x = log56/(6log2)