Problem 69 - Introductory and Intermediate Algebra for College Students 4th

Question

Let \(\log _{b} 2=A\) and \(\log _{b} 3=C .\) Write each expression in terms of \(A\) and \(C\). $$\log _{b} \frac{3}{2}$$

Step-by-Step Solution

Answer

The expression \(\log _{b} \frac{3}{2}\) in terms of A and C is \(C - A\).

Step 1: Apply the Logarithm Quotient Rule

The Quotient Rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator. So, we can rewrite \(\log _{b} \frac{3}{2}\) as \(\log _{b} 3 - \log _{b} 2\).

Step 2: Substitute Known Values

From the given expressions, we know that \(\log _{b} 2 = A\) and \(\log _{b} 3 = C\). Substituting these values into our previous expression, we get \(C - A\).