document.write( "Question 21507: I need help solving (2^x^2 / 2^x) = 64. I need to solve for x. THanks \n" ); document.write( "

Algebra.Com's Answer #10404 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
I hope I'm reading the problem correctly.\r
\n" ); document.write( "\n" ); document.write( "Solve for x:\r
\n" ); document.write( "\n" ); document.write( " $\"%282%5E%28x%5E2%29%29%2F2%5Ex+=+64\"$ Simplify the left side.
\n" ); document.write( " $\"2%5E%28x%5E2-x%29+=+64\"$ Substitute: $\"64+=+2%5E6\"$
\n" ); document.write( " $\"2%5E%28x%5E2-x%29+=+2%5E6\"$ The bases (2) are equal, therefore, the exponents are equal, thus:
\n" ); document.write( " $\"x%5E2-x+=+6\"$ Subtract 6 from both sides.
\n" ); document.write( " $\"x%5E2-x-6+=+0\"$ Solve by factoring.
\n" ); document.write( " $\"%28x%2B2%29%28x-3%29+=+0\"$ Apply the zero product principle.
\n" ); document.write( " $\"x%2B2+=+0\"$ and/or $\"x-3+=+0\"$
\n" ); document.write( "If $\"x%2B2+=+0\"$ then, $\"x+=+-2\"$
\n" ); document.write( "If $\"x-3+=+0\"$ then, $\"x+=+3\"$ \r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "x = -2
\n" ); document.write( " $\"%282%5E%28-2%29%5E2%29%2F2%5E%28-2%29+=+%282%5E4%29%2F2%5E%28-2%29\"$ Simplify:
\n" ); document.write( " $\"%282%5E4%29%282%5E2%29+=+2%5E6\"$ = 64 This checks.\r
\n" ); document.write( "\n" ); document.write( "x = 3
\n" ); document.write( " $\"%282%5E3%5E2%29%2F2%5E3+=+%282%5E9%29%2F2%5E3\"$ Simplify.
\n" ); document.write( " $\"%282%5E9%29%282%5E%28-3%29%29+=+2%5E6\"$ = 64 This checks. \n" ); document.write( "

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