# Solving exponent equation with same base being added

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 $$x$$?

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