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

Question

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

anonymous · Answer

It is solvable ,

anonymous · Answer

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

parthkohli · Answer

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

parthkohli · Answer

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

anonymous · Answer

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.

asnaseer · Answer

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.