Verify if the solution of the equation is real 4^x-2^x=12.

We notice that 4^x =
2^2x

We'll re-write the
equation:

2^2x - 2^x - 12 =
0

We'll replace 2^x by t:

t^2
- t - 12 = 0

We'll apply quadratic
formula:

t1 = [1+sqrt(1 +
48)]/2

t1 = (1 + 7)/2

t1 =
4

t2 = -3

But 2^x = t1
=> 2^x = 4 <=> 2^x = 2^2

Since the
bases are matching,we'll apply one to one rule:

x =
2.

2^x = t2 => 2^x = -3
impossible!

The equation has only one real
solution, namely x = 2.