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What is the result of logbA - logbC?

logb(A + C)

logb(A / C)

The expression logbA - logbC can be simplified using one of the fundamental properties of logarithms, known as the quotient rule. According to this rule, the difference of two logarithms with the same base can be expressed as the logarithm of the quotient of their arguments. In mathematical terms, the quotient rule states that:

logbA - logbC = logb(A / C).

This means that when you subtract the logarithm of C from the logarithm of A, you are effectively finding the logarithm of the division of A by C. This property is essential in both simplifying logarithmic expressions and solving equations involving logarithms.

Consequently, the correct answer showcases this important logarithmic property, demonstrating how logarithmic functions operate in relation to division and the relationships between their arguments.

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logb(A x C)

logb(A - C)

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