document.write( "Question 97794This question is from textbook Introducing Pure Mathematics
\n" ); document.write( ": help me pleasee!! Solve simultaneously:\r
\n" ); document.write( "\n" ); document.write( " $\"log+xy+=7\"$ , $\"log+%28x%2Fy%29=+10\"$ \r
\n" ); document.write( "\n" ); document.write( "so far ... if $\"log+%28base+10%29+%28x%2Fy%29=10\"$ this implies that $\"%28x%2Fy%29=10\"$
\n" ); document.write( "therfore, $\"x=10y\"$ ... thats all i got! \n" ); document.write( "

Algebra.Com's Answer #71130 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%2810%2C+%28xy%29%29+=7\"$ , $\"log+%2810%2C%28x%2Fy%29%29=+1\"$ Start with the given system\r
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\n" ); document.write( "\n" ); document.write( " $\"xy=10%5E7\"$ , $\"x%2Fy=+10%5E1\"$ Rewrite the logs using the property $\"log%28b%2Cx%29=y\"$ <==> $\"b%5Ey=x\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"xy=10000000\"$ , $\"x%2Fy=+10\"$ Rewrite $\"10%5E7\"$ as 10,000,000 for the first equation. Rewrite $\"10%5E1\"$ as 10 for the second equation\r
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\n" ); document.write( "\n" ); document.write( " $\"x=10y\"$ Solve the second equation for x by multiplying both sides by y\r
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\n" ); document.write( "\n" ); document.write( " $\"%2810y%29y=10000000\"$ Plug in $\"x=10y\"$ into the first equation. This will eliminate x so we can solve for y\r
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\n" ); document.write( "\n" ); document.write( " $\"10y%5E2=10000000\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"cross%2810%2F10%29y%5E2=10000000%2F10\"$ Divide both sides by 10\r
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\n" ); document.write( "\n" ); document.write( " $\"y%2Ay=1000000\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1000\"$ Take the square root of both sides. So this is our first answer\r
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\n" ); document.write( "\n" ); document.write( " $\"x=10%281000%29\"$ Plug in $\"y=1000\"$ into $\"x=10y\"$ to find x\r
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\n" ); document.write( "\n" ); document.write( " $\"x=10000\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( "So our answer is \r
\n" ); document.write( "\n" ); document.write( " $\"x=10000\"$ and $\"y=1000\"$ \r
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\n" ); document.write( "\n" ); document.write( "Check:\r
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\n" ); document.write( "\n" ); document.write( " $\"log+%2810%2C%28xy%29%29+=7\"$ Start with the first equation\r
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\n" ); document.write( "\n" ); document.write( " $\"log+%2810%2C%2810000%2A1000%29%29+=7\"$ Plug in $\"x=10000\"$ and $\"y=1000\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log+%2810%2C%2810000000%29%29+=1\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"7+=7\"$ Evaluate the left side. So the solutions $\"x=10000\"$ and $\"y=1000\"$ make the first equation true\r
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\n" ); document.write( "\n" ); document.write( "---------------------------------------------\r
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\n" ); document.write( "\n" ); document.write( " $\"log+%2810%2C%28x%2Fy%29%29+=1\"$ Start with the second equation\r
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\n" ); document.write( "\n" ); document.write( " $\"log+%2810%2C%2810000%2F1000%29%29+=1\"$ Plug in $\"x=10000\"$ and $\"y=1000\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"log+%2810%2C%2810%29%29+=1\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( " $\"1+=1\"$ Evaluate the left side. So the solutions $\"x=10000\"$ and $\"y=1000\"$ make the second equation true \n" ); document.write( "

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