Question

2^(2x)-3*(2^x)=-2 solve for x

Answer 1

Assume 2^x=a ............(1)
a^2-3a=-2 or a^2-3a+2=0. ..............(2)
This is quadratic equation, solve for a.
Once you find a, you can find x from (1).

Answer 2

So to begin solving the quadratic equation, would I divide both sides by three, so as to isolate the variables to the left?

Answer 3

Oh, nevermind- I'd get one side to equal zero, as you showed, then work from there.

Answer 4

I think it is an easy to factor quadratic equation. Just factor it.

Answer 5

(a-3)(a+1)... is this correct?

Answer 6

Nope, try again :)

Answer 7

a(a-3)?

Answer 8

No, your previous answer almost correct.
Here's how to think it:
From the quadratic eq, a=1, b=-3, c=2
find two number X and Y, where X*Y = a*c=2
and X+Y=b=-3
Give up?

Answer 9

(a-2)(a-1)

Answer 10

Yup, finally. Just do the rest.

Answer 11

(2x-2)(2x-1) ?

Answer 12

No, (a-2)(a-1)=0 means
a=2 or a=1 (we have two answer here)
2^x=2 or 2^x=1
x=2log2 or x=0

Answer 13

okay! Great!

One more question:
In the beginning, when we substituted 2^x for a, why did the first 2^x become a^2, while the one which was multiplied by the 3 was just "a"? Was this do to the quadratic form?

Answer 14

Thank you sooo much by the way!!! :)

Answer 15

2^(2x)=(2^x)^2=(2^2)^x
This is just exponential rule. Try it with numbers, you'll understand.