Final answer:
log₂ 16 and log₄ 64 are not equal; they are 4 and 3 respectively, because 2 raised to the 4th power equals 16 and 4 raised to the 3rd power equals 64.
Step-by-step explanation:
The question asks whether log₂ 16 and log₄ 64 are equal. To find out, we can evaluate each logarithm separately and then compare the results. Recall the definition of a logarithm: if logₓ x = y, then 3ⁿ = x. Thus, for log₂ 16, we are looking for the power to which 2 must be raised to get 16. Since 2⁴ = 16, it follows that log₂ 16 = 4. Similarly, for log₄ 64, we're looking for the power to which 4 must be raised to get 64, and since 4³ = 64, we find that log₄ 64 = 3. Therefore, log₂ 16 and log₄ 64 are not equal; they are 4 and 3, respectively.