document.write( "Question 149219: Solve: 2^(x+1)*8^(-x) =4 \n" ); document.write( "

Algebra.Com's Answer #109471 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for x:
\n" ); document.write( " $\"2%5E%28%28x%2B1%29%29+%2A+8%5E%28%28-x%29%29+=+4\"$ Rewrite this as:
\n" ); document.write( " $\"2%5E%28%28x%2B1%29%29%2F8%5Ex+=+4\"$ Multiply both sides by $\"8%5Ex\"$
\n" ); document.write( " $\"2%5E%28%28x%2B1%29%29+=+4%2A8%5Ex\"$ Recall that: $\"a%5En%2Aa%5Em+=+a%5E%28%28m%2Bn%29%29\"$ , so you can write:
\n" ); document.write( " $\"2%5Ex%2A2%5E1+=+4%2A8%5Ex\"$ Divde both sides by 2 to simplify a bit.
\n" ); document.write( " $\"2x+=+2%2A8%5Ex\"$ ,,,but $\"8%5Ex+=+%282%5E3%29%5Ex\"$ = $\"2%5E%28%283x%29%29\"$ Making this substitution, you get:
\n" ); document.write( " $\"2%5Ex+=+2%2A2%5E%28%283x%29%29\"$ = $\"2%5E%28%283x%2B1%29%29\"$ Now, because the bases (2) are equal, the exponents are equal, so...
\n" ); document.write( " $\"x+=+3x%2B1\"$ Solve for x:
\n" ); document.write( " $\"2x+=+-1\"$
\n" ); document.write( " $\"x+=+-%281%2F2%29\"$
\n" ); document.write( "Let's check this solition:
\n" ); document.write( " $\"2%5E%28%28x%2B1%29%29+%2A+8%5E%28-x%29+=+4\"$ Substitute $\"x+=+-%281%2F2%29\"$
\n" ); document.write( " $\"2%5E%28%28%28-1%2F2%29%2B1%29%29+%2A+8%5E%28%281%2F2%29%29+=+4\"$ Simplify the left side.
\n" ); document.write( " $\"2%5E%28%281%2F2%29%29+%2A+8%5E%28%281%2F2%29%29+=+4\"$ Substitute $\"8+=+2%5E3\"$
\n" ); document.write( " $\"2%5E%28%281%2F2%29%29+%2A+%282%5E3%29%5E%281%2F2%29+=+4\"$ Simplify.
\n" ); document.write( " $\"2%5E%28%281%2F2%29%29+%2A+2%5E%28%283%29%2F2%29+=+4\"$ Simplify.
\n" ); document.write( " $\"2%5E%281%2F2+%2B+3%2F2%29+=+4\"$
\n" ); document.write( " $\"2%5E%284%2F2%29+=+4\"$
\n" ); document.write( " $\"2%5E2+=+4\"$
\n" ); document.write( " $\"4+=+4\"$ \n" ); document.write( "

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