It's a secret. Not the same Base? Make it the same base and your life WILL be easier. Whoops, I let the secret out.
3(2^3X) = 5(4^2X-3)
if by 5(4^2x-3) you mean 5(4^(2x-3))
take common log of both sides, use product law of logarithms, use power law for logarithms (to bring the exponents down), factor x, and you should get x = (log5-log3-3log4)/(3log2-2log4) as an exact answer
if by 5(4^2x-3) you mean what you say, then i got x= (log15log3 - log5) / (2log4-3log2). method is the same as above