2^2x -2 x 2^x -8 = 0
Please help solve this equation.
Thank you very much
2^2x -2 x 2^x -8 = 0
I'm sure that is
2^(2x) -2(2^x) -8 = 0
In another form,
(2^x)^2 -2(2^x) -8 = 0 -----------(i)
(i) is a quadratic erquation in 2^x.
So if y = 2^x,
then (i) becomes
y^2 -2y -8 = 0
So,
(y -4)(y+2) = 0
y = 4 or -2
When y = 4,
2^x = 4
Take the natural logs of both sides,
x*ln(2) = ln(4)
x = ln(4) / ln(2)
x = 2ln(2) / ln(2)
x = 2 ----------------answer.
When y = -2,
2^x = -2
x*ln(2) = ln(-2)
There are no real values for logs of negative numbers, so reject this.