Final answer:
To evaluate log₄(√2), recognize that √2 can be written as 2^(1/2). Then apply the logarithm power rule, simplifying log₄(2) to 1/2 because 4 is 2^2. The final answer is (1/2) × (1/2) which equals 1/4.
Step-by-step explanation:
To evaluate the expression log₄(√2), we need to understand how logarithms work and apply the properties of logarithms.
The radical sign, √, indicates a square root, so √2 is equivalent to 2^(1/2). Therefore, we can rewrite the original expression as log₄(2^(1/2)).
We can then apply the property of logarithms which states that logₙ(x^y) = y × logₙ(x). This means that our expression simplifies to (1/2) × log₄(2).
Since 4 is 2 raised to the second power (2^2), log₄(2) simplifies to 1/2 because 2 is the base to the power that gives 4.
Finally, the expression is then (1/2) × (1/2) = 1/4.
So the evaluation of log₄(√2) is c. 1/4.