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Question

Evaluate the logarithm.

log6 1/36

Answer 1

To evaluate the logarithm log6 (1/36), we need to rewrite 1/36 as a power of 6.

1/36 = (1/6)^2

So, log6 (1/36) = log6 ((1/6)^2)

Using the properties of logarithms, we can rewrite this as:

log6 ((1/6)^2) = 2 * log6 (1/6)

Now, we can further simplify by using the property that loga (1/a) = -1:

2 * log6 (1/6) = 2 * (log6 1 - log6 6) = 2 * (0 - 1) = 2 * (-1) = -2

Therefore, log6 (1/36) = -2.