1.) 2^(x) = 3 ^(x-1)
2.) 3^(x+2) = 5^ ( x - 1)
2^x = 3^(x+1)
Take the natural log of both sides (any base will do, actually).
ln[2^x] = ln[3^(x+1)] <--- log[a^x] = x*log(a) for all bases.
x*ln(2) = (x+1)*ln(3)
x*[ln(2) - ln(3)] = ln(3)
x = ln(3)/[ln(2) - ln(3)] = -ln(3)/[ln(3) - ln(2)]
(The last step isn't really necessary, I just find it to be a bit tidier since x is negative.)
-Dan