Question 319892: Which is equivalent to 4 log3 a+3 log3(2b)-log3^m?
A)log3((2a^4b^3)/m)
B)log3((8a^4b^3)/m)
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! 4 log3 a+3 log3(2b)-log3^m?
Why did you include ^ in the term log3^m? It makes no sense unless this is a typo.
I think you meant to type: 4log3(a) + 3log(2b) - log3(m).
In any case, several log rules must be applied here.
For 4log3(a) + 3log(2b), we apply logb(mn) = logb(m) + logb(n). This is the multiplication of logs rule.
Then 4log3(a) + 3log(2b) becomes log3[(a^4*(2b)^3], which then becomes
log3(8a^4*b^3).
We now have log3(8a^4*b^3) - log3(m) for which we apply
logb(m/n) = logb(m) – logb(n). This is the division of logs rule.
Answer: log3[(8a^4*b^3)]/(m).
Copy and paste the following link to learn more about how to use the log rules:
http://www.purplemath.com/modules/logrules.htm
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