document.write( "Question 823929: Given that Log (base 4) 3y – 2 log (base 4) x – 1 = 0, express y in terms of x.
\n" ); document.write( "I hope you get the question right! \n" ); document.write( "

Algebra.Com's Answer #495928 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%284%2C+%283y%29%29+-+2log%284%2C+%28x%29%29+-+1+=+0\"$
\n" ); document.write( "First we will combine the logs. To do so we need to use a property of logarithms, $\"n%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5En%29%29\"$ , to \"move\" the 2 in front of the second log:
\n" ); document.write( " $\"log%284%2C+%283y%29%29+-+log%284%2C+%28x%5E2%29%29+-+1+=+0\"$
\n" ); document.write( "Now we can use another property of logs, $\"log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29\"$ , to combine the logs:
\n" ); document.write( " $\"log%284%2C+%28%283y%29%2Fx%5E2%29%29+-+1+=+0\"$

\n" ); document.write( "Now that we are down to one log, we will isolate it. Adding 1 to each side:
\n" ); document.write( " $\"log%284%2C+%28%283y%29%2Fx%5E2%29%29+=+1\"$
\n" ); document.write( "Next we rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+n\"$ is equivalent to $\"p+=+a%5En\"$ . Using this pattern on our equation we get:
\n" ); document.write( " $\"%283y%29%2Fx%5E2+=+4%5E1\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"%283y%29%2Fx%5E2+=+4\"$

\n" ); document.write( "Now that the logs are gone, we can solve for y. Multiplying both sides by $\"x%5E2\"$ :
\n" ); document.write( " $\"3y+=+4x%5E2\"$
\n" ); document.write( "Dividing by 3:
\n" ); document.write( " $\"y+=+%284x%5E2%29%2F3\"$ \n" ); document.write( "

\n" );