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Chapter 12: Problem 69

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

Short Answer

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

Step by step solution

01

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 \(\log _{b} 3 - \log _{b} 2\).
02

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 \(C - A\).

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\)

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