189. a) $\log _{2} 16$
b) $\log _{6} 36$
c) $\log _{8} 1$.
Solution. a) Here we need to find such an exponent $x$ that $2^{x}=16$. Solving this equation, we get $2^{x}=2^{4}$, hence $x=4$. Therefore, $\log _{2} 16=4$.

b) From the equation $6^{x}=36$ we find $6^{x}=6^{2}$, i.e., $x=2$. Thus, $\log _{6} 36=2$.

c) In this case, we have the equation $8^{x}=1$. This is only possible if $x=0$, hence $\log _{3} 1=0$.