SOLUTION: 1/2 log (base 3) of M + 3 log (base a) of N = 1 , express M in terms of N?

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Question 609113: 1/2 log (base 3) of M + 3 log (base a) of N = 1 , express M in terms of N?
Answer by lwsshak3(11628) About Me  (Show Source):
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1/2 log (base 3) of M + 3 log (base a) of N = 1 , express M in terms of N
1/2log3(M)+3loga(N)=1
convert to base 3
1/2log3(M)+log3(N^3)/log3(a)=1
place under single log
log3[√M*(N^(3/log3(a))]=1
convert to exponential form
3^1=√M*(N^(3/log3(a))=3
√M=3/(N^(3/log3(a))
square both sides
M=9/(N^(3/log3(a))^2
M=9/(N^(6/log3(a))