Question

Solve for x:
4^x - 6(2^x) + 8 = 0

Answer 1

\(\large\color{black}{ \displaystyle 4^x - 6(2^x) + 8 = 0 }\)

\(\large\color{black}{ \displaystyle (2\cdot 2)^x - 6(2^x) + 8 = 0 }\)

\(\large\color{black}{ \displaystyle 2^x\cdot 2^x - 6(2^x) + 8 = 0 }\)

\(\large\color{black}{ \displaystyle (2^x)^2 - 6(2^x) + 8 = 0 }\)

Answer 2

Then you can do the following substitution:

\(\large\color{black}{ \displaystyle w=2^x }\)

Answer 3

You will obtain a new equation:

\(\large\color{black}{ \displaystyle w^2 - 6w + 8 = 0 }\)

and this you can solve for w, and afterward substitute
these solutions for w into \(w=2^x\)

(note that any negative solution for w will be excluded because \(2^x\) is never negative)