document.write( "Question 815429: How do I get the following logarithm as a singke term that doesn't contain a logarithm
\n" ); document.write( "e^(9-6ln (x)+ln (y))
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Algebra.Com's Answer #490985 by jsmallt9(3758) $\"\"$ $\"About$

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$\"e%5E%289-6ln+%28x%29%2Bln+%28y%29%29\"$
\n" ); document.write( "Since $\"e%5Eln%28q%29+=+q\"$ we will be able to solve this problem if we change the 9 into a logarithm and then combine the logs. Since ln(e) = 1 we can rewrite the expression:
\n" ); document.write( " $\"e%5E%289ln%28e%29-6ln+%28x%29%2Bln+%28y%29%29\"$
\n" ); document.write( "Now we can use the $\"n%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5En%29%29\"$ property to move the two coefficients into the argument as its exponent:
\n" ); document.write( " $\"e%5E%28ln%28e%5E9%29-ln+%28x%5E6%29%2Bln+%28y%29%29\"$
\n" ); document.write( "Now we start combining the logs. For the first two we will use the $\"log%28a%2C+%28p%29%29-log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29\"$ property:
\n" ); document.write( " $\"%28e%5E%28ln%28e%5E9%2Fx%5E6%29%2Bln+%28y%29%29%29\"$
\n" ); document.write( "For the remaining logs we will use the $\"log%28a%2C+%28p%29%29%2Blog%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29\"$ property:
\n" ); document.write( " $\"e%5E%28ln%28%28e%5E9%2Fx%5E6%29%2Ay%29%29\"$
\n" ); document.write( "We now have the desired \"e to the ln\" form. So this equals:
\n" ); document.write( " $\"%28e%5E9%2Fx%5E6%29%2Ay%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"y%2Ae%5E9%2Fx%5E6\"$ \n" ); document.write( "

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