Question

2^x + 2 = 4^x - 1

Answer 1

If you are asked to solve for x. Then it is what you are going to do.
First, you know that \[4 = 2^2\], right?

Answer 2

Hence.
\[2^x + 2 = (2^2)^x -1\]
And
\[2^x + 2 = 2^{2x} -1\]
Then you will have
\[2^{2x} -2^x = 3\]
Okay. Let me stop here. Can you follow @kellington?

Answer 3

solve the quadratic
\[u^{2} -u-3 = 0\]
where
\[u = 2^{x}\]