document.write( "Question 934270: roots of 2^x + 12(2)^-x = 7 \n" ); document.write( "

Algebra.Com's Answer #567325 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+2%5Ex+%2B+12%282%29%5E%28-x%29+=+7+\"$
\n" ); document.write( "Multiply both sides by $\"+2%5Ex+\"$
\n" ); document.write( " $\"+2%5E%28+2x+%29+%2B+12+=+7%2A2%5Ex+\"$
\n" ); document.write( "Let $\"+z+=+2%5Ex+\"$
\n" ); document.write( " $\"+z%5E2+-+7z+%2B+12+=+0+\"$
\n" ); document.write( " $\"+%28+z+-+3+%29%2A%28+z+-+4+%29+=+0+\"$
\n" ); document.write( " $\"+z+=+3+\"$
\n" ); document.write( " $\"+z+=+4+\"$
\n" ); document.write( "-----------
\n" ); document.write( " $\"+2%5Ex+=+3+\"$
\n" ); document.write( " $\"+x%2Alog%282%29+=+log%283%29+\"$
\n" ); document.write( " $\"+x+=+log%283%29+%2F+log%282%29+\"$
\n" ); document.write( "By my calculator:
\n" ); document.write( " $\"+x+=+1.585+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+2%5Ex+=+4+\"$
\n" ); document.write( " $\"+x%2Alog%282%29+=+log%284%29+\"$
\n" ); document.write( " $\"+x+=+log%284%29+%2F+log%282%29+\"$
\n" ); document.write( " $\"+x+=+2+\"$
\n" ); document.write( "--------------
\n" ); document.write( "The roots are $\"+x+=+1.585+\"$ , $\"+x+=+2+\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"+2%5Ex+%2B+12%282%29%5E%28-x%29+=+7+\"$
\n" ); document.write( " $\"+2%5E1.585+%2B+12%282%29%5E-1.585+=+7+\"$
\n" ); document.write( " $\"+3.00008+%2B+12%2A.33332+=+7+\"$
\n" ); document.write( " $\"+3+%2B+4+=+7+\"$
\n" ); document.write( "OK
\n" ); document.write( "and, also
\n" ); document.write( " $\"+2%5E2+%2B+12%282%29%5E-2+=+7+\"$
\n" ); document.write( " $\"+4+%2B+12%2A%281%2F4%29+=+7+\"$
\n" ); document.write( " $\"+4+%2B+3+=+7+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );