SOLUTION: Need some help with logarithm: thanks for helping in advance, I really appreciate it. Rewrite the expression 2 log3(x+3)-5log 3(2x-1)+log3 5, as a single logarithm with coeffici

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Need some help with logarithm: thanks for helping in advance, I really appreciate it. Rewrite the expression 2 log3(x+3)-5log 3(2x-1)+log3 5, as a single logarithm with coeffici      Log On

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Question 603113: Need some help with logarithm: thanks for helping in advance, I really appreciate it.
Rewrite the expression 2 log3(x+3)-5log 3(2x-1)+log3 5, as a single logarithm with coefficient 1. Assume all variables represent positive real numbers for which all logs are defined.

Answer by KMST(1863) About Me  (Show Source):
You can put this solution on YOUR website!
I assume your expression was
2%2Alog%283%2C%28x%2B3%29%29-5%2Alog+%283%2C%282x-1%29%29%2Blog%283%2C5%29 where each "3" was the base of a logarithm.
You must have learned properties of logarithms such as
log%28b%2C%28a%5Em%29%29=m%2Alog%28b%2C%28a%29%29
log%28b%2C%28a%2Ac%29%29=log%28b%2C%28a%29%29%2Blog%28b%2C%28c%29%29
log%28b%2C%28a%2Fc%29%29=log%28b%2C%28a%29%29-log%28b%2C%28c%29%29
You can read those properties from right to left, too, because the equal sign is a two-way street.
So 2%2Alog%283%2C%28x%2B3%29%29=log%283%2C%28x%2B3%29%5E2%29, and you can apply all of those properties to transform your expression, like this: