Homework Help: Precalc

Posted by Amy on Thursday, January 27, 2011 at 5:20pm.

How to solve for x:

2^(2x) + 2^(x) -12 = 0

Steps too

I tried solving this but I ended with ln(12) / 2ln(2) + ln(2) but the real answer is supposed to be ln(3) / ln(2) or 1.585

Precalc - Reiny, Thursday, January 27, 2011 at 5:39pm
let 2^x= y
then your equation becomes
y^2 + y - 12 = 0
(y+4)(y-3) = 0
so y = -4 or y = 3
then
2^x= -4, which is not possible
or
2^x = 3
ln both sides
ln(2x) = ln3
x ln2 = ln 3
x = ln3/ln2 = appr. 1.58

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