solve 3^x=4^(x-2)
take ln of both sides
ln (3^x) = ln (4^(x-2))
x(ln3) = (x-2)(ln4)
= x(ln4) - 2ln4
xln3 - xln4 = -2ln4
x(ln3 - ln4) = -2ln4
x = -2ln4/(ln3-ln4)
or
x = 2ln4/(ln4 - ln3)
if get appr. 9.638
check:
3^9.638 = appr. 39672.63
4^7.638 = 39676.6
----- close enough using only 3 decimals, if I use my calculator's memory and store the full value of x, my error is 5.9x10^-6