SOLUTION: What is M equal to in: log{{{6}}}(3m+7) - log{{{6}}}(m+4) = 2log{{{6}}}6 - 3log{{{6}}}3 I was thinking that you add log{{{6}}}(m+4) to both sides, but i believe that isn't right.

Question 20558: What is M equal to in: log(3m+7) - log(m+4) = 2log6 - 3log3 I was thinking that you add log(m+4) to both sides, but i believe that isn't right.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
log(3m+7) - log(m+4) = 2log6 - 3log3 I was thinking that you add log(m+4) to both sides, but i believe that isn't right.
use the formula log x to base y =log x/log y where all logs are to any common base.
so we get {(log (3m+7)/log 6)}-{(log (m+4)/log 6)}={(2 log 6/log 6) -(3 log 3/log 6)}
now multiply through out with log 6 to get
log (3m+7)-log (m+4)=2log 6-3log 3
now use the formula log x^n = n*log x
and log(x/y)=log x-log y
log ((3m+7)/(m+4))=log 6*6-log 3*3*3=log 36-log 27=log(36/27)
taking antilogs on both sides
((3m+7)/(m+4))=36/27=4/3
cross multiplying
3(3m+7)=4(m+4)
9m+21=4m+16
9m-4m=16-21=-5
5m=-5
m=-1

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