document.write( "Question 733342: 32^(4x-1) = 16^(3x)\r
\n" ); document.write( "\n" ); document.write( "Trying to help my son with his algebra 11 homework. I have no idea about this one. Help! \n" ); document.write( "

Algebra.Com's Answer #448361 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+32%5E%28+4x-1+%29+=+16%5E%283x%29+\"$ is this it? If so,
\n" ); document.write( "Note that $\"+32+=+2%5E5+\"$ and $\"+16+=+2%5E4+\"$
\n" ); document.write( "Now write this as:
\n" ); document.write( " $\"+%28+2%5E5+%29%5E%28+4x-1+%29+=+%28+2%5E4+%29%5E%28+3x+%29+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "Now use the general rule:
\n" ); document.write( " $\"+%28a%5Eb%29%5Ec++=+a%5E%28b%2Ac%29+\"$
\n" ); document.write( " $\"+2%5E%28+5%2A%28+4x-1+%29+%29+=+2%5E%28+4%2A3x+%29+\"$
\n" ); document.write( "For the equation to be true, the exponents on
\n" ); document.write( "both sides have to be equal, so
\n" ); document.write( " $\"+5%2A%28+4x-1+%29+=+12x+\"$
\n" ); document.write( " $\"+20x+-+5+=+12x+\"$
\n" ); document.write( " $\"+8x+=+5+\"$
\n" ); document.write( " $\"+x+=+5%2F8+\"$
\n" ); document.write( "------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+32%5E%28+4x-1+%29+=+16%5E%283x%29+\"$
\n" ); document.write( " $\"+32%5E%28+4%2A%285%2F8%29+-+1+%29+=+16%5E%283%2A%285%2F8%29%29+\"$
\n" ); document.write( " $\"+32%5E%28+5%2F2+-+1+%29+=+16%5E%28+15%2F8+%29+\"$
\n" ); document.write( " $\"+32%5E%28+3%2F2+%29+=+16%5E%28+15%2F8+%29+\"$
\n" ); document.write( "square both sides
\n" ); document.write( " $\"+32%5E3+=+16%5E%28+15%2F4+%29+\"$
\n" ); document.write( " $\"+32%5E3+=+2%5E15+\"$
\n" ); document.write( " $\"+32768+=+32768+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );