In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

Verified step by step guidance

1. Identify the given exponential equation: \(13^y = 874\).
2. Recall the definition of a logarithm: If \(a^b = c\), then \(\log_a(c) = b\).
3. Apply the definition to the given equation: Here, \(a = 13\), \(b = y\), and \(c = 874\).
4. Rewrite the equation in logarithmic form: \(\log_{13}(874) = y\).
5. Verify that the rewritten equation correctly represents the original exponential relationship.

Key Concepts

Exponential Equations

Exponential equations are mathematical expressions in which a variable appears in the exponent. In the equation 13^y = 874, 13 is the base, y is the exponent, and 874 is the result of the exponential expression. Understanding how to manipulate these equations is crucial for converting them into logarithmic form.

Logarithmic Form

Logarithmic form is a way to express exponential equations using logarithms. The equation a^b = c can be rewritten as log_a(c) = b, where 'a' is the base, 'b' is the exponent, and 'c' is the result. This transformation is essential for solving equations involving exponents and understanding their properties.

Properties of Logarithms

Properties of logarithms include rules that govern how logarithms can be manipulated, such as the product, quotient, and power rules. These properties help simplify logarithmic expressions and solve equations. Familiarity with these rules is important when converting between exponential and logarithmic forms.