SOLUTION: How can I write the following expression as a single term that does not contain a logarithm : e^6-6ln(x)+ln(y)

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Question 863300: How can I write the following expression as a single term that does not contain a logarithm : e^6-6ln(x)+ln(y)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We will use the identities

(1)     a%5E%28b%2Bc%2Bd%29=a%5Eb%2Aa%5Ec%2Aa%5Ed

(2)     e%5Eln%28A%29=A

(3)     ln%28a%5Eb%29=b%2Aln%28a%29

e%5E%286-6%2Aln%28x%29%2Bln%28y%29%29

Use (1)

e%5E6%2Ae%5E%28-6%2Aln%28x%29%29%2Ae%5Eln%28y%29%29

Use (2) on the third factor:

e%5E6%2Ae%5E%28-6%2Aln%28x%29%29%2Ay%29

Use (3) on the exponent of the second factor:

matrix%282%2C1%2C%22%22%2Ce%5E6%2Ae%5E%28ln%28x%5E%28-6%29%29%29%2Ay%29

Use (2) on the second factor:

e%5E6%2Ax%5E%28-6%29%2Ay%29

That doesn't contain a logarithm, so it would do.
Maybe you might want to go further and get rid of the
negative exponent:

e%5E6%2Ay%2Fx%5E6%29

Edwin