SOLUTION: 1/2 log(base3) of M + 3log(bases)ofN=1,express M in terms of N.

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Question 1174281: 1/2 log(base3) of M + 3log(bases)ofN=1,express M in terms of N.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


log rules:
(1) log(ab) = log(a)+log(b)
(2) log(a^n) = n*log(a)

1/2 log(base 3) of M = log(base 3) of M^(1/2) (rule (1))
3log(base 3) of N = log(base 3) of N^3 (rule (1))

log(base 3) of M^(1/2) + log(base 3) of N^3 = log(base 3) of ((M^1/2)(N^3)) (rule 2)

Now the equation is

log(base 3) of ((M^1/2)(N^3)) = 1

Translating that to exponential form gives us

(M^1/2)(N^3) = 3^1 = 3

Solving for M in terms of N:

{M)(N^6) = 9 (squaring both sides)
M = 9/N^6