Evaluate the following expressions. (a) $\log _{5} 5^{3}=$ (b) $\log _{2} 16=$ (c) $\log _{5} 625=$ (d) $\log _{4} 4^{9}=$

Step 1 ：The logarithm base b of a number x is the exponent to which b must be raised to get x. In other words, if y = log_b(x), then b^y = x. So, for each of the expressions, we need to find the exponent that the base must be raised to in order to get the number inside the logarithm.

Step 2 ：For (a), we need to find the exponent to which 5 must be raised to get 5^3. Since 5^3 = 125, we need to find the exponent to which 5 must be raised to get 125.

Step 3 ：For (b), we need to find the exponent to which 2 must be raised to get 16.

Step 4 ：For (c), we need to find the exponent to which 5 must be raised to get 625.

Step 5 ：For (d), we need to find the exponent to which 4 must be raised to get 4^9.

Step 6 ：Let's calculate these values.

Step 7 ：For (a), the result is 3.0000000000000004 instead of 3. This is due to the precision limitations of floating point arithmetic. We can safely round this to 3 as the difference is negligible.

Step 8 ：Final Answer: (a) $\log _{5} 5^{3}=\boxed{3}$ (b) $\log _{2} 16=\boxed{4}$ (c) $\log _{5} 625=\boxed{4}$ (d) $\log _{4} 4^{9}=\boxed{9}$