document.write( "Question 174793: If ((log_3)2) = x, simplify :\r
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Algebra.Com's Answer #129887 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"log%283%2C%286%2Asqrt%282%29%29%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"log%283%2C%286%29%29%2Blog%283%2C%28sqrt%282%29%29%29\"$ Break up the log using the identity $\"log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Alog%28b%2C%28B%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%283%2C%286%29%29%2Blog%283%2C%28%282%29%5E%281%2F2%29%29%29\"$ Convert from radical to exponential notation.\r
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\n" ); document.write( "\n" ); document.write( " $\"log%283%2C%286%29%29%2B%281%2F2%29log%283%2C%282%29%29\"$ Rewrite the second log 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( " $\"log%283%2C%286%29%29%2B%281%2F2%29x\"$ Replace $\"log%283%2C%282%29%29\"$ with \"x\"\r
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\n" ); document.write( "\n" ); document.write( "So $\"log%283%2C%286%2Asqrt%282%29%29%29\"$ simplifies to $\"log%283%2C%286%29%29%2B%281%2F2%29x\"$ where $\"x=log%283%2C%282%29%29\"$ \n" ); document.write( "

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