SOLUTION: How do I get the following logarithm as a singke term that doesn't contain a logarithm e^(9-6ln (x)+ln (y))

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Question 815429: How do I get the following logarithm as a singke term that doesn't contain a logarithm
e^(9-6ln (x)+ln (y))
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
e%5E%289-6ln+%28x%29%2Bln+%28y%29%29
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:
e%5E%289ln%28e%29-6ln+%28x%29%2Bln+%28y%29%29
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:
e%5E%28ln%28e%5E9%29-ln+%28x%5E6%29%2Bln+%28y%29%29
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:
%28e%5E%28ln%28e%5E9%2Fx%5E6%29%2Bln+%28y%29%29%29
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:
e%5E%28ln%28%28e%5E9%2Fx%5E6%29%2Ay%29%29
We now have the desired "e to the ln" form. So this equals:
%28e%5E9%2Fx%5E6%29%2Ay%29
or
y%2Ae%5E9%2Fx%5E6