Final answer:
The logarithmic form of the equation 8³ = 512 is log₈ 512 = 3, as it expresses that base 8 is raised to the power 3 to result in 512.
Step-by-step explanation:
The logarithmic form of 8³ = 512 is log₈ 512 = 3. This is because logarithms express the exponent as the result of the log function when the base (here 8) is raised to that exponent to get the number (512). To understand logarithms, remember that the equation aⁿ = b can be rewritten in logarithmic form as loga b = n. For the equation 8³ = 512, we can say that the base 8 is raised to the power of 3 to get 512. Hence, in logarithmic form, it is written as log₈ 512 = 3. This is based on the property of logarithms where the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.