document.write( "Question 464917: Solve for x: 2^(2x) + 2^(x+2) - 12 = 0, I do believe logarithms are to be used to simplify. \n" ); document.write( "

Algebra.Com's Answer #318665 by stanbon(75887) $\"\"$ $\"About$

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Solve for x: 2^(2x) + 2^(x+2) - 12 = 0,
\n" ); document.write( "I do believe logarithms are to be used to simplify
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\n" ); document.write( "(2^x)^2 + (2^x)*4 - 12 = 0
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\n" ); document.write( "(2^x)^2 + 4*(2^x) - 12 = 0
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\n" ); document.write( "Note: Quadratic form with variable 2^x
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\n" ); document.write( "Let 2^x = w
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\n" ); document.write( "w^2 + 4w - 12 = 0
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\n" ); document.write( "Factor:
\n" ); document.write( "(w+6)(w-2) = 0
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\n" ); document.write( "w = -6 or w = 2
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\n" ); document.write( "Solve for \"x\":
\n" ); document.write( "2^x = -6 or 2^x = 2
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\n" ); document.write( "Note: No power of 2 can be negative so 2^x = -6 is meaningless.
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\n" ); document.write( "2^x = 2
\n" ); document.write( "x = 1 (this is the only solution for the problem)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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