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# log MN=log + log

how do i work problem logMN=log      + log

### 5 Answers by Expert Tutors

Ali M. | Friendly and High Quality TutoringFriendly and High Quality Tutoring
4.8 4.8 (4 lesson ratings) (4)
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let log (M) + log(N) = x then 10 ^ [ log(M) + log (N) ] = 10 ^ x. so simplifying we get

10 ^ log(M) *10 ^ log(N) = M*N = 10 ^ x. further simplification we get

log(MN) = x = log(M)  + log (N)

Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (331 lesson ratings) (331)
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A simple derivation:

logb MN = logb (blogb M blogb N) = logb blogb M + logb N = logb M + logb N.

Jack M. | Keys to Chemistry, Calculus, Literature and MoreKeys to Chemistry, Calculus, Literature...
4.7 4.7 (309 lesson ratings) (309)
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Nastassia ---

The other answers by Will and Robert are correct.

I would just add an example:

log 12  =  log 4 + log 3  OR  log 6 + log 2, or even log 9 + log (4/3).  Try those on your caluclator.

If you have something like log 3x, it would be log 3 + log x.

Will M. | Chemistry tutor who gets that teachers don't get it.Chemistry tutor who gets that teachers d...
4.9 4.9 (59 lesson ratings) (59)
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If I understand the question, this is just a property of logs.  The log of a product is the sum of the logs.

log (M * N) = log (M) + log (N)

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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logMN=logM + logN. This is the log property for production.