We can write the argument of the logarithm as a power of 6:
[tex]\log_6\dfrac1{36}=\log_6\dfrac1{6^2}=\log_66^{-2}[/tex]
Then using the property that [tex]\log_ba^n=n\log_ba[/tex], we get
[tex]\log_6\dfrac1{36}=-2\log_66[/tex]
and since [tex]6=6^1[/tex], we have [tex]\log_66=1[/tex], so the value of this expression is simply -2.
