Question

I need help solving:
4^x +4^(-x) =5/2
The answer is x=1/2,x=-1/2, but I can't see it.

Answer 1

o.O

Answer 2

4^x + 4^(-x) = 5/2
Replace 4^x with u, move 5/2 to the LHS and combine fractions\[\frac{((-2+u) (-1+2 u))}{2 u}=0 \]Replace u with 4^x and solve each factor for x.\[4^x=2,2^{2x}=2^1,x=1/2 \]\[4^x=1/2,2^{2x}=2^{-1},2x=-1,x=-\frac{1}{2}\]

Answer 3

Thank you very much. This makes perfect sense.