A financial analyst is simplifying a ratio of investment returns using the logarithmic expression $\log_b \frac{R_1}{R_2}$. To expand this expression for a report, which of the following represents the correct application of the Quotient Property of Logarithms?

A production analyst uses logarithms to linearize ratios when comparing the efficiency of different manufacturing shifts. Match each logarithmic expression with its correctly expanded and simplified form according to the Quotient Property of Logarithms.

A laboratory researcher is simplifying a concentration ratio expressed as $\log_5 \frac{5}{c}$. The researcher uses the Quotient Property of Logarithms to rewrite this as $\log_5 5 - \log_5 c$, which then simplifies to ${}1 - \log_5 c$.

True or False: The researcher has correctly applied the property to simplify the expression.

Troubleshooting Logarithmic Expansions in Financial Reports

Expanding Logarithmic Intensity Ratios

An operations analyst at a retail company is evaluating the ratio of monthly online sales, $S_1$, to in-store sales, $S_2$, using the logarithmic expression $\log \frac{S_1}{S_2}$. To expand this expression for a regional performance report, the analyst applies the Quotient Property of Logarithms.

According to this property, the logarithm of the quotient is equal to the logarithm of the numerator ____ the logarithm of the denominator.

A quality control specialist at a beverage manufacturing plant is monitoring the acidity ratio of a new fruit juice blend. The ratio is represented by the logarithmic expression $\log_2 \frac{d}{16}$, where $d$ is the acid concentration in milligrams per liter. To simplify the quality control database formula, the specialist needs to expand and simplify this expression using the Quotient Property of Logarithms.

Arrange the steps in the correct order to expand and simplify the expression $\log_2 \frac{d}{16}$.