Write each equation in its equivalent exponential form. 4 = log₂ 16

Verified step by step guidance

1. Recall the definition of logarithm: if \(y = \log_{b} x\), then the equivalent exponential form is \(b^{y} = x\).
2. Identify the base \(b\), the exponent \(y\), and the result \(x\) from the given equation \(4 = \log_{2} 16\).
3. Here, the base \(b\) is 2, the exponent \(y\) is 4, and the result \(x\) is 16.
4. Apply the definition by rewriting the logarithmic equation as an exponential equation: \$2^{4} = 16$.
5. This shows the equivalent exponential form of the given logarithmic equation.

Key Concepts

Definition of Logarithms

A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log₂ 16 means the exponent to which 2 must be raised to get 16.

Conversion Between Logarithmic and Exponential Forms

Logarithmic and exponential forms are two ways to express the same relationship. The equation log_b a = c is equivalent to the exponential form b^c = a, where b is the base, c is the exponent, and a is the result.

Properties of Exponents

Understanding how exponents work helps verify conversions. For example, knowing that 2^4 = 16 confirms that log₂ 16 = 4, reinforcing the connection between logarithms and exponents.