Evaluate (without use of a calculator). (a) $\log _{8} 4+\log _{4} 16=$

Step 1 ：Given the expression \(\log _{8} 4+\log _{4} 16\)

Step 2 ：We can use the logarithm properties to simplify the expression. The properties are as follows: \(\log_b{a^n} = n\log_b{a}\) and \(\log_b{a} + \log_b{c} = \log_b{ac}\)

Step 3 ：For the first term, \(\log_8{4}\), we can rewrite 4 as \(2^2\) and 8 as \(2^3\). Then we can use the first property to simplify the expression.

Step 4 ：For the second term, \(\log_4{16}\), we can rewrite 16 as \(4^2\). Then we can use the first property to simplify the expression.

Step 5 ：By simplifying, we get \(\log_8{4} = \frac{2}{3}\) and \(\log_4{16} = 2\)

Step 6 ：Adding these two values, we get \(\frac{2}{3} + 2 = \frac{8}{3}\)

Step 7 ：Final Answer: \(\boxed{\frac{8}{3}}\)