In Exercises 9–20, write each equation in its equivalent logarithmic form. 7^y = 200

Key Concepts

Exponential Equations

Exponential equations are mathematical expressions where a variable appears in the exponent. In the equation 7^y = 200, 7 is the base, y is the exponent, and 200 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, 'c' is the result, and 'b' is the exponent. This transformation is essential for solving equations involving exponents and understanding their properties.

Properties of Logarithms

Properties of logarithms include rules that simplify the manipulation of logarithmic expressions, such as the product, quotient, and power rules. These properties help in solving logarithmic equations and understanding their behavior. Familiarity with these rules is important when converting between exponential and logarithmic forms.