How do you solve #2^(2x) + 2^(x + 2) - 12 = 0#?

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Answer 1 · 2015-10-25T15:00:09

#x=1#

First, rearrange the equation like this:

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

#(2^x)^2 + 4(2^x) - 12 = 0#

Now, treat this like a quadratic equation by substituting #2^x=s#:

#s^2+4s-12=0#

#(s+6)(s-2)=0#

#s=-6# or #s=2#

Now, go back to the substitution:

#2^x=s#

#2^x=-6# or #2^x=2#

Since #2^x# can never equal a negative number, we can rule out the first solution.

However, the second solution results in #x=1#

Hope that helped