document.write( "Question 25373: If 5^x=3 and 9^y=125, find the value of xy. \n" ); document.write( "
Algebra.Com's Answer #13632 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
If 5^x=3 and 9^y=125, find the value of xy.\r\n" );
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document.write( "For the first equation\r\n" );
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document.write( "     5x = 3\r\n" );
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document.write( "Take the log of both sides\r\n" );
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document.write( "log(5x) = log(3)\r\n" );
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document.write( "Use the rule of logs on LHS:  logAB = BｷlogA\r\n" );
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document.write( "xｷlog5 = log3\r\n" );
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document.write( "Divide both sides by log5\r\n" );
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document.write( "    log3   \r\n" );
document.write( "x = 覧覧 \r\n" );
document.write( "    log5  \r\n" );
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document.write( "====\r\n" );
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document.write( "For the second equation\r\n" );
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document.write( "      9y = 125\r\n" );
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document.write( "Take the log of both sides\r\n" );
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document.write( " log(9y) = log125\r\n" );
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document.write( "As before, use the rule of logs on LHS:  logAB = BｷlogA\r\n" );
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document.write( "yｷlog9 = log125\r\n" );
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document.write( "Divide both sides by log9\r\n" );
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document.write( "    log125\r\n" );
document.write( "y = 覧覧覧\r\n" );
document.write( "     log9 \r\n" );
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document.write( "        log3   log125\r\n" );
document.write( "So xy = 覧覧 ｷ 覧覧覧\r\n" );
document.write( "        log5    log9\r\n" );
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document.write( "But we can simplify that\r\n" );
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document.write( "log3   log125\r\n" );
document.write( "覧覧 ｷ 覧覧覧\r\n" );
document.write( "log5    log9\r\n" );
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document.write( "write 125 as 53 and 9 as 32\r\n" );
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document.write( "log3   log53\r\n" );
document.write( "覧覧 ｷ 覧覧覧\r\n" );
document.write( "log5   log32\r\n" );
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document.write( "Again we use the rule  logAB = BｷlogA \r\n" );
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document.write( "log3   3log5\r\n" );
document.write( "覧覧 ｷ 覧覧覧\r\n" );
document.write( "log5   2log3\r\n" );
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document.write( "Cancel the log3's\r\n" );
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document.write( " 1\r\n" );
document.write( "log3   3log5\r\n" );
document.write( "覧覧 ｷ 覧覧覧\r\n" );
document.write( "log5   2log3\r\n" );
document.write( "         1    \r\n" );
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document.write( "Cancel the log5's\r\n" );
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document.write( " 1        1\r\n" );
document.write( "log3   3log5\r\n" );
document.write( "覧覧 ｷ 覧覧覧\r\n" );
document.write( "log5   2log3\r\n" );
document.write( " 1        1    \r\n" );
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document.write( "All that's left is\r\n" );
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document.write( " 3\r\n" );
document.write( "覧予r\n" );
document.write( " 2\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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