Question

1. evaluate \\(\log_{4}(\sqrt{2})\\)

Explanation:

Express the base and argument as powers of 2

$$
LATEXBLOCK0
$$

Apply the change of base formula

$$ \log_{4}(\sqrt{2}) = \frac{\log_2(2^{\frac{1}{2}})}{\log_2(2^2)} $$

Simplify the logarithmic expression

$$ \log_{4}(\sqrt{2}) = \frac{\frac{1}{2}}{2} = \frac{1}{4} $$

Answer:

\(\frac{1}{4}\)