Question

how to solve for x ? 4^x - 2^x - 12 = 0

Answer 1

\[4^{x} - 2^{x} - 12 = 0\]

Answer 2

hint : take 2^x as y
then 4^x = y^2
and you will get a quadratic in 'y'
which you can solve easily :)

Answer 3

so i will be getting y=4 and y=-3 . how do I find x when y= -3 ?

Answer 4

@hartnn

Answer 5

It would be rejected, unless you wanna use De Moivre's Theorem to get some complex number.

Answer 6

lets stick with real domain and so y=4
2^x =4
can you find x from here ?

Answer 7

x = 2 ? @hartnn

Answer 8

thats it!

Answer 9

so when y = -3 , x is invalid ?

Answer 10

If and only if you stick to the real domain that is...

Answer 11

yes,
as 2^x cannot be negative for a real value of x
its always >0