Solve the equation 8^(x-1) = 6^(3x) . Express your answer in terms of ln 2 and ln3 .
8(x-1) = 63x
23(x-1) = (2 * 3)3x
23x * 2-3 = 23x * 33x / : 23x
2-3 = 33x / ln
ln(2-3) = ln(33x)
-3 ln(2) = 3x ln(3) / :3
- ln(2) = x ln(3)
x = - ln(2)/ln(3)
8(x-1) = 63x
23(x-1) = (2 * 3)3x
23x * 2-3 = 23x * 33x / : 23x
2-3 = 33x / ln
ln(2-3) = ln(33x)
-3 ln(2) = 3x ln(3) / :3
- ln(2) = x ln(3)
x = - ln(2)/ln(3)
