In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C. logb (3/2)

Key Concepts

Logarithmic Properties

Logarithmic properties are rules that govern the manipulation of logarithms. Key properties include the quotient rule, which states that logb(m/n) = logb(m) - logb(n), and the product rule, which states that logb(mn) = logb(m) + logb(n). Understanding these properties is essential for rewriting logarithmic expressions in simpler forms.

Change of Base Formula

The change of base formula allows us to express logarithms in terms of logarithms of different bases. Specifically, logb(x) can be rewritten as logk(x) / logk(b) for any positive k. This concept is useful when converting logarithmic expressions to a more manageable form, especially when dealing with different bases.

Logarithmic Relationships

Logarithmic relationships involve understanding how different logarithmic values relate to each other. In this case, we have logb(2) = A and logb(3) = C. By recognizing that logb(3/2) can be expressed as logb(3) - logb(2), we can substitute A and C to rewrite the expression in terms of A and C, facilitating easier calculations.