Final answer:
To change the logarithmic statement to an equivalent statement involving an exponent, we can say that 6 raised to the power of 3 is equal to 216.
Step-by-step explanation:
To change the logarithmic statement to an equivalent statement involving an exponent, we need to remember the relationship between logarithms and exponents. The logarithm of a number raised to an exponent is equal to the product of the exponent and the logarithm of the number.
In this case, we have log₆(216) = 3. To rewrite this using exponents, we can say that 6 raised to the power of 3 is equal to 216. So, 6^3 = 216.
When changing a logarithmic statement to an equivalent exponential statement, we can use the definition of logarithms. The statement log₆(216) = 3 means that 6 raised to the power of 3 equals 216. Therefore, the equivalent exponential statement is 6³ = 216.
This conversion is based on the fundamental property of logarithms: if logₓ(b) = x, then aˣ = b. Here, a is the base of the logarithm, b is the number whose logarithm is taken, and x is the value of that logarithm.
Understanding this property allows us to solve logarithmic equations and convert logarithmic expressions into exponential form, which is useful in many areas of mathematics, including algebra and calculus.