Is the correct answer x = (5 ln 3 - 2 ln 4) : (ln 4-2 ln3)
4^(x +2) = 3^(2x +5)
(x +2)ln(4) = (2x +5)ln(3)
x*ln(4) +2ln(4) = 2x*ln(3) +5ln(3)
x[ln(4) -2ln(3)] = 5ln(3) -2ln(4)
x = [5ln(3) -2ln(4)] / [ln(4) -2ln(3)] ------your solution.
If you want to go on simplifying that, here is one way,
x = [ln(3^5) -ln(4^2)] / [ln(4) -ln(3^2)]
x = [ln(243) -ln(16)] / [ln(4) -ln(9)]
Since ln(a/b) = ln(a) -ln(b), then,
x = [ln(243/16)] / [ln(4/9)] --------------answer.
By calculator,
x = -3.354755646