Final answer:
Expression log₅[(x/4)²] is equivalent to 2 log₅(x) + log₅(16), by using properties of logarithms to simplify the expression.
Step-by-step explanation:
The student has asked which expression is equivalent to log₅[(x/4)²]. To solve this, we will apply logarithmic properties. Using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can say that log₅[(x/4)²] = 2 · log₅(x/4). Then, applying the property that the logarithm of the division of two numbers is the difference between the logarithms of the two numbers, we get 2 · (log₅(x) - log₅(4)). Simplifying this, we get the equivalent expression 2 log₅(x) - 2 log₅(4). Since log₅(4) is a constant, and 2 log₅(4) = log₅(16), we can rewrite the expression as 2 log₅(x) + log₅(16), which matches option B.