document.write( "Question 236461: Let a= log x, b = log y and c = log z
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Algebra.Com's Answer #174038 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"log%28%28%28x%5E2%2Asqrt%28y%29%29%2Fz%5E3%29%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"log%28%28x%5E2%2Asqrt%28y%29%29%29-log%28%28z%5E3%29%29\"$ Break up the log using the identity $\"log%28b%2C%28A%2FB%29%29=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%28%28x%5E2%29%29%2Blog%28%28sqrt%28y%29%29%29-log%28%28z%5E3%29%29\"$ Break up the first log using the identity $\"log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%28%28x%5E2%29%29%2Blog%28%28y%5E%281%2F2%29%29%29-log%28%28z%5E3%29%29\"$ Convert to rational exponent notation.\r
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\n" ); document.write( "\n" ); document.write( " $\"2log%28%28x%29%29%2B%281%2F2%29log%28%28y%29%29-3log%28%28z%29%29\"$ Pull down the exponents using the identity $\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2a%2B%281%2F2%29b-3c\"$ Now use the equations $\"a=log%28%28x%29%29\"$ , $\"b=log%28%28y%29%29\"$ , and $\"c=log%28%28z%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"log%28%28%28x%5E2%2Asqrt%28y%29%29%2Fz%5E3%29%29=2a%2B%281%2F2%29b-3c\"$ where $\"a=log%28%28x%29%29\"$ , $\"b=log%28%28y%29%29\"$ , and $\"c=log%28%28z%29%29\"$ \n" ); document.write( "

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