Final answer:
To find the equivalent values of the given logarithm log₂(8¹³/³), we apply the properties of logarithms. The equivalent value is 13 log₂(2).
Step-by-step explanation:
To find the equivalent values of the logarithm log₂(8¹³/³), we can apply the properties of logarithms. According to the property log(a/b) = log(a) - log(b), we can rewrite the given logarithm as log₂(8¹³) - log₂(³). Next, we can simplify the logarithms: log₂(8¹³) is equal to 13 log₂(8), and log₂(³) is equal to log₂(2³).
Using the formula log(aᵇ) = b log(a), we can further simplify the expressions as 13 log₂(2³) - 3 log₂(2³). Breaking down the exponents, we have 13 log₂(8) - 3 log₂(8). Since 8 is 2³, we can simplify it to 13 log₂(2) - 3 log₂(2).
Therefore, the equivalent value of the given logarithm is 13 log₂(2) - 3 log₂(2), which can be rewritten as 13log₂(2) - 3log₂(2). Hence, the correct answer is d. 13 log₂(2).