Evaluate the logarithm.

Question

log6 1/36

Answer 1

To evaluate the logarithm log6 (1/36), we need to determine the exponent to which we need to raise 6 in order to obtain 1/36.

6^x = 1/36

To simplify 1/36, we can rewrite it as 1/(6^2):

6^x = 1/(6^2)
6^x = 6^(-2)

Since the bases of both sides of the equation are equal, we can conclude that the exponents must be equal as well:

x = -2

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