document.write( "Question 149752: log r - log t + 2 log s \n" ); document.write( "

Algebra.Com's Answer #109855 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%2810%2C%28r%29%29-log%2810%2C%28t%29%29%2B2log%2810%2C%28s%29%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%28r%29%29-log%2810%2C%28t%29%29%2Blog%2810%2C%28s%5E2%29%29\"$ Rewrite $\"2log%2810%2C%28s%29%29\"$ as $\"log%2810%2C%28s%5E2%29%29\"$ using the identity $\"y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%28r%2Ft%29%29%2Blog%2810%2C%28s%5E2%29%29\"$ Combine the logs using the identity $\"log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%28%28r%2Ft%29%28s%5E2%29%29%29\"$ Combine the logs using the identity $\"log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%28rs%5E2%2Ft%29%29%29\"$ Simplify.\r
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\n" ); document.write( "\n" ); document.write( "So $\"log%2810%2C%28r%29%29-log%2810%2C%28t%29%29%2B2log%2810%2C%28s%29%29\"$ simplifies to $\"log%2810%2C%28rs%5E2%2Ft%29%29%29\"$ \n" ); document.write( "

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