document.write( "Question 611748: 2Log Y base 3 + 2Log X base 3= 4, find y in terms of x? \n" ); document.write( "

Algebra.Com's Answer #385150 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2log%283%2C+%28y%29%29+%2B+2log%283%2C+%28x%29%29=+4\"$
\n" ); document.write( "To solve for y, we need to \"extract\" it from the logarithm. For this, let's start by using properties of logs to combine the two logs. First the coefficients have to go. The easy way for this is to divide both sides of the equation by 2:
\n" ); document.write( " $\"log%283%2C+%28y%29%29+%2B+log%283%2C+%28x%29%29=+2\"$

\n" ); document.write( "Next we can use a property of logs, $\"log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29\"$ , to combine the logs. (This property requires logs with coefficients of 1. This is why the 2's had to go earlier.)
\n" ); document.write( " $\"log%283%2C+%28y%2Ax%29%29=+2\"$

\n" ); document.write( "Now we rewrite the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"a%5Eq+=+p\"$ . Using this pattern on our equation we get:
\n" ); document.write( " $\"3%5E2+=+y%2Ax\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( "9 = y*x

\n" ); document.write( "Now that the logs are gone, the equation is simple to solve for y. Divide both sides by 9:
\n" ); document.write( " $\"9%2Fx+=+y\"$
\n" ); document.write( "And we're finished! \n" ); document.write( "

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