SOLUTION: Greetings, Please help solve this problem. Use the properties of logarithms to rewrite each expression as a single logarithm with coefficient 1. Assume that all variables represe

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Greetings, Please help solve this problem. Use the properties of logarithms to rewrite each expression as a single logarithm with coefficient 1. Assume that all variables represe      Log On


   

Question 813798: Greetings,
Please help solve this problem. Use the properties of logarithms to rewrite each expression as a single logarithm with coefficient 1. Assume that all variables represent positive real numbers.
4 over 3 1n m - 2 over 3 1n 8n - 1n m^3n^2
I used ^ to show the those numbers are up.
Hoping you'll be able to solve. Thank you very much!!!!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4 over 3 1n m - 2 over 3 1n 8n - 1n m^3n^2
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^ is commonly used for exponents.
It's LN, for natural log, no 1n.
There's nothing to solve, only combine and simplify.
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%284%2F3%29ln%28m%29+-+%282%2F3%29ln%288n%29+-+ln%28m%5E3n%5E2%29
Many opportunities for error, wish us luck.
= %281%2F3%29ln%28m%5E4%29+-+%281%2F3%29ln%2864n%5E2%29+-+ln%28m%5E3n%5E2%29
= %281%2F3%29ln%28m%5E4%2F%2864n%5E2%29%29+-+ln%28m%5E3n%5E2%29
= %281%2F3%29ln%28m%5E4%2F%2864n%5E2%29%29+-+%281%2F3%29ln%28m%5E9n%5E6%29
= %281%2F3%29ln%28m%5E4%2F%2864m%5E9n%5E8%29%29
= %281%2F3%29ln%281%2F%2864m%5E5n%5E8%29%29
= ln%28root%283%2C%281%2F%2864m%5E5n%5E8%29%29%29%29
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= ln%28root%283%2Cmn%29%2F%284m%5E2n%5E3%29%29%29