SOLUTION: Mental math evaluation the logarithms log3 1/27

Question 964056: Mental math evaluation the logarithms log3 1/27
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
L3(1/27) = y if and only if 3^y = 1/27

1/27 is equal to 1/3^3 which is equal to 3^(-3)

3^y = 3^(-3) if and only if y = -3.

therefore L3(1/27) = -3.

L3 means log to the base of 3.

you get L3(1/27) = -3 if and only if 3^(-3) = 1/27

since 3^(-3) = 1/3^3 and since 1/3^3 = 1/27, then the solution is confirmed.

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