In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16

Verified step by step guidance

1. Understand that the equation given is in logarithmic form: \(4 = \log_2 16\).
2. Recall the definition of a logarithm: \(\log_b a = c\) means \(b^c = a\).
3. Identify the base \(b\), the result \(a\), and the exponent \(c\) from the logarithmic equation: here, \(b = 2\), \(a = 16\), and \(c = 4\).
4. Rewrite the equation in exponential form using the identified values: \(2^4 = 16\).
5. Verify the conversion by calculating \(2^4\) to ensure it equals 16, confirming the exponential form is correct.

Key Concepts

Logarithms

Logarithms are the inverse operations of exponentiation. The logarithm log_b(a) answers the question: 'To what exponent must the base b be raised to produce a?' In the given equation, log₂ 16 indicates the power to which 2 must be raised to yield 16.

Exponential Form

Exponential form expresses a logarithmic equation as an exponent. For example, the equation log_b(a) = c can be rewritten in exponential form as b^c = a. This transformation is essential for solving logarithmic equations and understanding their relationships with exponential functions.

Base of a Logarithm

The base of a logarithm is the number that is raised to a power to obtain a given value. In the expression log₂ 16, the base is 2. Understanding the base is crucial for converting logarithmic expressions into their exponential counterparts, as it determines the relationship between the logarithm and the exponent.