4^(2x) -4^(x-1) -12 = 0
Cannot take the logs of both sides because log(0) is undefined or there are no log(0). So,
4^(2x) -4^(x-1) = 12
Take the logs of both sides,
2x*log(4) -(x-1)log(4) = log(12)
2x*log(4) -x*log(4) +log(4) = log(4*3)
x*log(4) +log(4) = log(4) +log(3)
x*log(4) = log(3)
x = log(3) / log(4) --------------answer.
Or, x = (1/2)[log(3) / log(2)]
Yes.
[I just took a peek. I'm home for a while.]
Log of the original LHS is not as I wrte it. I fell on the trap.
log(a +b) is not log(a) +log(b), as I warned in another reply before.
And, normally I check my answer against the original equation, quickly or in "scratch paper" or calculator, before I say that is my answer. I forgot to do that this morning before I left for work.