Question
32(2)^2x-12(2)^x+1=0
I've spent too much time trying to figure this out. Please help.
I've spent too much time trying to figure this out. Please help.
Answers
Steve
32(2)^2x-12(2)^x+1=0
Recall that 2^2x = (2^x)^2, so you have
32(2^x)^2 - 12(2^x) + 1 = 0
Now, just to make things easier to read, let u = 2^x and you have
32u^2 - 12u + 1 = 0
(8u-1)(4u-1) = 0
u = 1/8 or 1/4
So, that means we have
2^x = 1/8 ------> x = -3
2^x = 1/4 ------> x = -2
Recall that 2^2x = (2^x)^2, so you have
32(2^x)^2 - 12(2^x) + 1 = 0
Now, just to make things easier to read, let u = 2^x and you have
32u^2 - 12u + 1 = 0
(8u-1)(4u-1) = 0
u = 1/8 or 1/4
So, that means we have
2^x = 1/8 ------> x = -3
2^x = 1/4 ------> x = -2