[tex] 2^{3x-7}= 5^{x-4} [/tex]
by taking log for both sides
[tex]log 2^{3x-7} = log 5^{x-4} [/tex]
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
[tex]x = \frac{7log2 - 4log5}{3log2 - log5} [/tex]
by using calculator
x ≈ -3.37
