Solving exponential equations by logs

[KatieLynn]

Homework Statement

2^(2x) + 2 ^(x) - 12 = 0

Homework Equations

none really

The Attempt at a Solution

so I think what you have to do is factor it
so it would be like

(2^x- )(2^x + )

then you set the factor equal to zero and solve for x but I'm not sure how to factor it.

 

[rocomath]

let u=2^x

now can you factor it?

 

[kbaumen]

Also notice that 2^2x = (2^x)^2
as previously mentioned u = 2^x, (u > 0, because the exponential function is always positive) so you get u^2 + u - 12 = 0, which is easy to solve. Just don't forget that u > 0.

 

[rocomath]

also, it would serve you well to remember the graph of "e" and "ln"