3^(x+4)=6^(2x-5) Solve the equation.

3^(x+4) = 6^(2x-5)
To solve, take the natural logarithm of both sides.
ln (3^(x+4)) = ln (6^(2x-5))
To simplify each side, apply the logarithm rule ln (a^m) =m*ln(a) .
(x+4)ln(3) = (2x-5) ln (6)
xln(3)+4ln(3) = 2xln(6) - 5ln(6)
Then, bring together the terms with x on one side of the equation. Also, bring together the terms without x on the other side of the equation.
xln(3) - 2xln(6) = -4ln(3) -5ln(6)
At the left side, factor out the GCF.
x(ln(3) - 2ln(6)) =-4ln(3) -5ln(6)
And, isolate the x.
x = (-4ln(3) - 5ln(6))/(ln(3)-2ln(6))
x~~5.374
Therefore, the solution is x~~5.374 .