Fill in the blanks.
To solve exponential and logarithmic equations, you can use the One-to-One and Inverse Properties below.
(a) $a^{x}=a^{y}$ if and only if ______.
(b) $\log _{a} x=\log _{a} y$ if and only if _______.
(c) $a^{\log _{a} x}=$ ______
(d) $\log _{a} a^{x}=$ ______