Solve 5^(x+2)=6^(3-x)

I tried taking the log of both sides but don't seem to be getting anywhere

5^(x + 2) = 6^(3 - x)

Take the natural log of each side:

ln(5^(x + 2)) = ln(6^(3 - x))

Using log rules, we get:

(x + 2)ln(5) = (3 - x)ln(6)

Distribute:

xln(5) + 2ln(5) = 3ln(6) - xln(6)

Move x-pieces to one side and numbers to the other:

xln(5) - xln(6) = 3ln(6) - 2ln(5)

Factor out an x:

x * (ln(5) - ln(6)) = 3ln(6) - 2ln(5)

Divide, and we have our solution:

x = (3ln(6) - 2ln(5)) / (ln(5) - ln(6))

Cleaned up:

x = (ln(216) - ln(25)) / (ln(5) - ln(6))

Finally:

x = ln(216/25) / ln(5/6)

5^(x+2)=6^(3-x)
(x+2)ln5=(3-x)ln6
xln5+2ln5=3ln6-xln6
x(ln5+ln6)=3ln6-2ln5
x=(3ln6-2ln5)/(ln5+ln6)