1. The size relationship of the following three numbers $\frac{3}{2}, \log _{16} 82, \log _{27} 124$ is ( ).
(A) $\frac{3}{2}<\log _{16} 82<\log _{27} 124$
(B) $\frac{3}{2}<\log _{27} 124<\log _{16} 82$
(C) $\log _{27} 124<\frac{3}{2}<\log _{16} 82$
(D) $\log _{27} 124<\log _{16} 82<\frac{3}{2}$
- 1.C.

Since $\log _{16} 82>\log _{16} 81=\log _{2} 81^{\frac{1}{4}}=\log _{2} 3$ $\log _{7} 124\frac{3}{2}$. Let $y=\log _{3} 5$, then $3^{y}=5$.
And $3^{\frac{3}{2}}=\sqrt{27}>5=3^{y}$, so, $y<\frac{3}{2}$.
In summary, $\log _{27} 124<\frac{3}{2}<\log _{16} 82$.