Question

solve this equation.

2^(2x) + 2^(x+2) - 96 = 0

x=

Answer 1

one can write 2^(2x) = (2^x)^2
say a=2^x then the equation becomes
a^2+4a-96=0;
a^2+12a-8a-96=0;
a(a+12)-8(a+12)=0
(a-8)(a+12)=0
so a=8 or a=-12.
solution #1. 2^x=8...2^x=2^3...x=3
solution #2. 2^x=-12. there is no solution for x in this case.
SO the only solution is that x=3