Solving exponent equation with same base being added

Question

I need to find $x$ from this equation: $$4^{x+1} + 4^{1-x} = 10$$

Since this is an addition and not multiplication, I cannot add the exponents. I do recognise that I will most likely have to use logarithms to solve this, but I cannot figure out how to manipulate the equation. I tried taking logs of both sides and writing it all in terms of base $4$ but that did not help.

Any help on how to solve for $x$?

Answer 1

Write your equation in the form $$4\cdot 4^x+\frac{4}{4^x}=10$$ and substitute $$t=4^x$$, now solve the quadratic.