Expert: Abe Mantell - 8/20/2010

Question
Hello!  I was wondering if you could help me solve for x in this equation:

4^x+4^(-x)= 5/2

I've tried to turn the equation into a log but that doesn't seem to be helping.  Any ideas?

Thanks!
Jenny

Answer
Hello Jenny,

The equation can be written as: 4^x + 1/(4^x) = 5/2
Now let y=4^x, to get: y + 1/y = 5/2
Multiplying by 2y: 2y^2 + 2 = 5y
===> 2y^2 - 5y + 2 =0
Which factors: (2y-1)(y-2)=0
==> 2y-1=0 or y-2=0
==> y=1/2 or y=2
==> 4^x=1/2 or 4^x=2
==> x= -1/2 or x=1/2

OK?

Abe