Question

4^x - 2^x = 3
Solution? Is it unsolvable?

Answer 1

It is solvable ,

Answer 2

Can you show the source of the question ( snapshot ) ?

Answer 3

\[\implies \left(2^x\right)^2 - (2^x) = 3\]

Answer 4

\[\implies (2^x)^2 - (2^x) = 3\]\[\implies (2^x)^2 - (2^x) - 3 =0\]Find the solutions of this quadratic. Ignore the negative solutions as \(2^x\) cannot be negative.

Answer 5

Tried using the quadratic formula. I ended up with
(2^x +- 2^x * sqrt(3)) / 4^x = 0
and I cannot seem to get anywhere else from that.
Also I have tried entering this into wolfram/mathway and it gives no solution or impossible solutions.

Answer 6

If you use the hints provided by @ParthKohli then you should find a valid solution.

It might help if you substituted: \(y=2^x\) and solved for \(y\) first.