Question

I'm not sure how to solve this question.

I know the answer's x≈-3.374, just don't know how they got it.

Answer 1

`2^(3x-7)= 5^(x-4)`

by taking log for both sides


`log 2^(3x-7) = log 5^(x-4)`

using log rule to simplify and solve

(3x-7)log2 = (x-4)log5

3xlog2 - 7log2 = xlog5 - 4log5

3xlog2 - xlog5 = 7log2 - 4log5

x(3log2 - log5) = 7log2 - 4log5


`x = (7log2 - 4log5)/(3log2 - log5)`

by using calculator

x ≈ -3.37