SOLUTION: Dear Sir/Madam, Please help me with this logarithm question, If logMN = logNM, M將, M, N ˃ 0, M and N ≠ 1, then MN. note: the base in logMN is M and the base

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Dear Sir/Madam, Please help me with this logarithm question, If logMN = logNM, M將, M, N ˃ 0, M and N ≠ 1, then MN. note: the base in logMN is M and the base       Log On


   

Question 894864: Dear Sir/Madam,
Please help me with this logarithm question,
If logMN = logNM, M將, M, N ˃ 0, M and N ≠ 1, then MN.
note: the base in logMN is M and the base in logNM is N

Thank you very much!
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
log MN = log NM, then
log base M (M) + log base M (N) = log base N (N) + log base N (M)
note log base M (M) = 1 and log base N (N) = 1, and
1 + log base M (N) = 1 + log base N (M)
subtract 1 from both sides of =
log base M (N) = log base N (M)
use change of base formula
log base M (N) = (log base N (N)) / (log base N (M))
1 / log base N (M) = log base N (M)
1 = (log base N (M))^2
1 = log base N (M)
implies that N = M
NM = N^2 or M^2