In Exercises 9–20, write each equation in its equivalent logarithmic form. b^3 = 1000

Key Concepts

Exponential Form

Exponential form expresses a relationship where a base raised to an exponent equals a number. In the equation b^3 = 1000, 'b' is the base, '3' is the exponent, and '1000' is the result. Understanding this form is crucial for converting to logarithmic form.

Logarithmic Form

Logarithmic form is the inverse of exponential form, representing the exponent as a logarithm. The equation b^3 = 1000 can be rewritten in logarithmic form as log_b(1000) = 3, indicating that 'b' raised to the power of '3' equals '1000'. This transformation is essential for solving equations involving exponents.

Change of Base Formula

The change of base formula allows the conversion of logarithms from one base to another, which is useful when the base is not easily computable. It states that log_b(a) = log_k(a) / log_k(b) for any positive k. This concept is important when working with logarithmic equations that require different bases for simplification or calculation.