Final answer:
The correct logarithmic form of the equation x³=216 is log_x(216) = 3. By solving the equation, we find that x equals 6.
Step-by-step explanation:
To convert the equation x³=216 into logarithmic form, we use the fact that if a¹ = b, then log_b(a) = n. Thus, we have several options:
a. log_x(216) = 3 is the correct logarithmic form since x raised to the power of 3 equals 216.
b. log_216(x) = 3 is incorrect because it suggests 216 raised to the power of 3 equals x, which is not our case.
c. log_3(x) = 216 is incorrect because it suggests 3 raised to the power of x equals 216.
d. log_x(3) = 216 is incorrect because it suggests x raised to the power of 216 equals 3.
The correct logarithmic form of the equation x³=216 is log_x(216) = 3, and by solving the original equation, we find that x equals the cube root of 216, which is x = 6.