document.write( "Question 144421: write as a single logarithm
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Algebra.Com's Answer #105226 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-3%2Alog%282%2C%282x%29%29\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-log%282%2C%28%282x%29%5E3%29%29\"$ Rewrite $\"3%2Alog%282%2C%282x%29%29\"$ as $\"log%282%2C%28%282x%29%5E3%29%29\"$ 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( " $\"log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-log%282%2C%288x%5E3%29%29\"$ Cube $\"2x\"$ to get $\"8x%5E3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%282%2C%283y%5E5%29%29-log%282%2C%288x%5E3%29%29\"$ Combine the first two 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( " $\"log%282%2C%28%283y%5E5%29%2F%288x%5E3%29%29%29\"$ 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( "So $\"log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-3%2Alog%282%2C%282x%29%29\"$ simplifies to $\"log%282%2C%28%283y%5E5%29%2F%288x%5E3%29%29%29\"$ \n" ); document.write( "

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