Solve the equation 8^(x-1) = 6^(3x) . Express your answer in terms of ln 2 and ln3 .

8^(x-1) = 6^3x

2^3(x-1) = (2 * 3)^3x

2^3x * 2^-3 = 2^3x * 3^3x        / : 2^3x

2^-3 = 3^3x                             / ln

ln(2^-3) = ln(3^3x)

-3 ln(2) = 3x ln(3)         / :3

- ln(2) = x ln(3)

x = - ln(2)/ln(3)