document.write( "Question 85475: I need to express log3x+6(logx-logy) as a single logarithm, and simplify if possible. I am not sure how to deal with the 6. This problem is from a handout, so there is no text information. \n" ); document.write( "

Algebra.Com's Answer #61700 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%2810%2C3x%29%2B6%2A%28log%2810%2C%28x%29%29-log%2810%2C%28y%29%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%283x%29%29%2B6%2A%28log%2810%2C%28x%2Fy%29%29%29\"$ Combine the inner logs by using $\"log%28b%2Cx%29-log%28b%2Cy%29=log%28b%2Cx%2Fy%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C3x%29%2Blog%2810%2C%28x%2Fy%29%5E6%29\"$ Use the identity $\"a%2Alog%28b%2Cx%29=log%28b%2Cx%5Ea%29\"$ to rewrite $\"6%2Alog%2810%2Cx%2Fy%29\"$ into $\"log%2810%2C%28x%2Fy%29%5E6%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C3x%29%2Blog%2810%2C%28x%5E6%2Fy%5E6%29%29\"$ Distribute the exponent\r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C3x%2A%28x%5E6%2Fy%5E6%29%29\"$ Combine the logs using $\"log%28b%2Cx%29%2Blog%28b%2Cy%29=log%28b%2Cx%2Ay%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log%2810%2C%283x%5E7%2Fy%5E6%29%29\"$ Multiply \n" ); document.write( "

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