Which of the following statements about logarithms is true?

The statement that logarithms have properties that relate to operations such as multiplication and division is fundamental in understanding how logarithmic expressions work.

In particular, the correct answer demonstrates one of the key properties of logarithms known as the quotient rule. This rule states that the logarithm of a quotient of two numbers is equal to the difference of the logarithms of the individual numbers. In mathematical terms, this is expressed as:

[ \log_b \left( \frac{x}{y} \right) = \log_b(x) - \log_b(y) ]

This property is essential for simplifying logarithmic expressions and solving equations involving logarithms. It tells us that if you have a fraction ( \frac{x}{y} ), you can represent its logarithm as the difference of the logarithms of the numerator and denominator.

Understanding this property allows one to manipulate logarithmic equations effectively, which is a crucial skill in higher mathematics, including algebra and calculus.