Take note whats in bold how do I factor out 2^x-1 out of the left side of the equation?
here's the deal: when you factor a power out of a polynomial, which power do you factor out: the smallest common power, or the biggest common power?
that's right, the smallest one. if you have x^5 - x^2, you only factor out x^2, not x^5.
analogy:
on this problem, just factor out 2^(x - 2).
this gives
left hand side = [2^(x - 2)](2^2 - 1)
= [2^(x - 2)](3)
you can then cancel the 3's, leaving 2^(x - 2) = 2^13. therefore, x - 2 = 13, so x = 15.
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