document.write( "Question 1168571: 2 log x base 5 + 3 log y base 3 = 8
\n" ); document.write( "6 log x base 5 - 2 log y base 3 = 2
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Algebra.Com's Answer #793154 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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2 log x base 5 + 3 log y base 3 = 8
\n" ); document.write( "6 log x base 5 - 2 log y base 3 = 2
\n" ); document.write( ":
\n" ); document.write( " $\"2%2Alog%285%2C%28x%29%29+%2B+3%2Alog%283%2C%28y%29%29+=+8\"$
\n" ); document.write( " $\"6%2Alog%285%2C%28x%29%29+-+2%2Alog%283%2C%28y%29%29+=+2\"$
\n" ); document.write( ":
\n" ); document.write( "Multiply the first equation by 3, subtract the 2nd equation
\n" ); document.write( " $\"6%2Alog%285%2C%28x%29%29+%2B+9%2Alog%283%2C%28y%29%29+=+24\"$
\n" ); document.write( " $\"6%2Alog%285%2C%28x%29%29+-+2%2Alog%283%2C%28y%29%29+=+2\"$
\n" ); document.write( "-----------------------------------------Subtraction eliminate the 1st term
\n" ); document.write( " $\"0+%2B+11%2Alog%283%2C%28y%29%29+=+22\"$
\n" ); document.write( "divide both sides by 11
\n" ); document.write( " $\"log%283%2C%28y%29%29+=+2\"$
\n" ); document.write( "the exponent equiv of logs
\n" ); document.write( " $\"y+=+3%5E2\"$
\n" ); document.write( "y = 9
\n" ); document.write( "then find x
\n" ); document.write( " $\"2%2Alog%285%2C%28x%29%29+%2B+3%2Alog%283%2C%289%29%29+=+8\"$
\n" ); document.write( "we know that $\"log%283%2C%289%29%29\"$ = 2
\n" ); document.write( " $\"2%2Alog%285%2C%28x%29%29+%2B+3%2A2+=+8\"$
\n" ); document.write( " $\"2%2Alog%285%2C%28x%29%29+=+8-6\"$
\n" ); document.write( " $\"2%2Alog%285%2C%28x%29%29+=+2\"$
\n" ); document.write( "divide both sides by 2
\n" ); document.write( " $\"log%285%2C%28x%29%29+=+1\"$
\n" ); document.write( "exponent equiv of logs
\n" ); document.write( "x = 5\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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