document.write( "Question 841628: If $\"lg+x%5E2y=a\"$ and $\"lg+%28x%2Fy%29+=+b\"$ , express $\"lg+%28y%2Fx%5E2%29\"$ in terms of a and b. \n" ); document.write( "

Algebra.Com's Answer #507099 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
First Equation,
\n" ); document.write( " $\"log%28x%5E2y%29=a\"$
\n" ); document.write( " $\"2log%28x%29%2Blog%28y%29=a\"$
\n" ); document.write( "-
\n" ); document.write( "Second Equation,
\n" ); document.write( " $\"log%28x%2Fy%29=b\"$
\n" ); document.write( " $\"log%28x%29-log%28y%29=b\"$
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\n" ); document.write( "Those give a system of equations in unknowns log(x) and log(y), which can be solved.
\n" ); document.write( "SYSTEM:
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\n" ); document.write( "2log(x)+log(y)=a
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\n" ); document.write( "log(x)-log(y)=b
\n" ); document.write( "---------------------\r
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\n" ); document.write( "\n" ); document.write( "Elimination Method will be most efficient.
\n" ); document.write( "Add left members and add right members.
\n" ); document.write( " $\"3log%28x%29=a%2Bb\"$
\n" ); document.write( " $\"highlight%28log%28x%29=%28a%2Bb%29%2F3%29\"$ ----Knowing this, find the formula for log(y).
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\n" ); document.write( " $\"log%28x%29-log%28y%29=b\"$
\n" ); document.write( " $\"log%28x%29-b=log%28y%29\"$
\n" ); document.write( " $\"log%28y%29=log%28x%29-b\"$
\n" ); document.write( " $\"log%28y%29=%28a%2Bb%29%2F3-b\"$ -----used substitution
\n" ); document.write( " $\"log%28y%29=%28%28a%2Bb%29-3b%29%2F3\"$
\n" ); document.write( " $\"highlight%28log%28y%29=%28a-2b%29%2F3%29\"$
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\n" ); document.write( "Almost done, ready to deal with the expression you want to transform.
\n" ); document.write( "SUMMARY:
\n" ); document.write( " $\"highlight%28log%28x%29=%28a%2Bb%29%2F3%29\"$ and $\"highlight%28log%28y%29=%28a-2b%29%2F3%29\"$
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\n" ); document.write( "The target expression to transform,
\n" ); document.write( " $\"highlight_green%28log%28y%2Fx%5E2%29%29\"$
\n" ); document.write( " $\"log%28y%29-2log%28x%29\"$
\n" ); document.write( "Now substitute what were found for log(x) and log(y).
\n" ); document.write( " $\"%28a%2Bb%29%2F3-2%28a-2b%29%2F3\"$
\n" ); document.write( " $\"%28a%2Bb%29%2F3-%282a-4b%29%2F3\"$
\n" ); document.write( " $\"%28a%2Bb-2a%2B4b%29%2F3\"$
\n" ); document.write( " $\"highlight%28highlight%28%28-a%2B5b%29%2F3%29%29\"$ \n" ); document.write( "

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