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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)

David G. GCSE Maths tutor, IB Maths tutor

2 years ago

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