Question

Solve

4^x + 15(4)^-x = 8

Answer 1

Let 4^x = y. Then your equation can be rewritten

y + 15/y = 8
or
y^2 -8y +15 = 0
which factors to
(y-5)(y-3) = 0

y = 5 or 3
If y = 4^x = 3, then x ln 4 = ln 3
x = ln 3/ln 4 = 0.7925

Now solve for the other root (when y=5) yourself.