How to solve $16^x-10\cdot4^x+16=0$

Question

I am unsure how to go about solving this equation to find x. Any help greatly appreciated.

Answer 1

Let $4^x=t$, then $16^x=(4^x)^2=t^2$

So, your equation will be $$t^2-10t+16=0$$ which is a simple quadratic equation.

Solve for $t$ first and then solve for $x$ ($\because 4^x=t $)