document.write( "Question 251388: log9^3 \n" ); document.write( "

Algebra.Com's Answer #183055 by jim_thompson5910(35256) $\"\"$ $\"About$

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Since $\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29\"$ we can rewrite $\"log%2810%2C%289%5E3%29%29\"$ as $\"3%2Alog%2810%2C%289%29%29\"$ . So $\"log%2810%2C%289%5E3%29%29=3%2Alog%2810%2C%289%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Edit: If the log looks like this: $\"log%289%2C%283%29%29\"$ , then disregard the last portion\r
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\n" ); document.write( "\n" ); document.write( "Let $\"y=log%289%2C%283%29%29\"$ . Using the property $\"log%28b%2C%28x%29%29=y\"$ <=> $\"b%5Ey=x\"$ , we can rewrite $\"y=log%289%2C%283%29%29\"$ as $\"9%5Ey=3\"$ . \r
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\n" ); document.write( "\n" ); document.write( "Now rewrite 9 as $\"3%5E2\"$ and 3 as $\"3%5E1\"$ to get $\"%283%5E2%29%5Ey=3%5E1\"$ and multiply the exponents to get $\"3%5E%282y%29=3%5E1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since the bases are equal, the exponents are equal. So $\"2y=1\"$ giving us the solution of $\"y=1%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since $\"y=log%289%2C%283%29%29\"$ , this means $\"log%289%2C%283%29%29=1%2F2\"$ which is our answer. \n" ); document.write( "

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