Final answer:
The value of log6(1/36) is approximately 1.7782.
Step-by-step explanation:
The value of log6(1/36) can be found by using the property of logarithms that log(a/b) equals log(a) - log(b). In this case, we have log6(1/36) = log6(1) - log6(36). Since log6(1) is equal to 0, we only need to determine log6(36).
Because 36 lies between 6 and 216 (which have logarithms of 1 and 3, respectively), we can estimate that the logarithm of 36 is approximately 1.7782.