SOLUTION: Express in terms of sums and differences of logarithms logₐ x^3y^2z (after the log is a) Can anyone help me solve this?

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Question 150412: Express in terms of sums and differences of logarithms
logₐ x^3y^2z (after the log is a)
Can anyone help me solve this?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28a%2C%28x%5E3y%5E2z%29%29 Start with the given expression.


log%28a%2C%28x%5E3%29%29%2Blog%28a%2C%28y%5E2z%29%29 Break up the log log%28a%2C%28x%5E3y%5E2z%29%29 using the identity log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Alog%28b%2C%28B%29%29



log%28a%2C%28x%5E3%29%29%2Blog%28a%2C%28y%5E2%29%29%2Blog%28a%2C%28z%29%29 Break up the log log%28a%2C%28y%5E2z%29%29 using the identity log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Alog%28b%2C%28B%29%29


3%2Alog%28a%2C%28x%29%29%2Blog%28a%2C%28y%5E2%29%29%2Blog%28a%2C%28z%29%29 Rewrite log%28a%2C%28x%5E3%29%29 as 3%2Alog%28a%2C%28x%29%29 using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


3%2Alog%28a%2C%28x%29%29%2B2%2Alog%28a%2C%28y%29%29%2Blog%28a%2C%28z%29%29 Rewrite log%28a%2C%28y%5E2%29%29 as 2%2Alog%28a%2C%28y%29%29 using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


So log%28a%2C%28x%5E3y%5E2z%29%29 expands to 3%2Alog%28a%2C%28x%29%29%2B2%2Alog%28a%2C%28y%29%29%2Blog%28a%2C%28z%29%29