Simplify/Condense log of 21- log of 3

Problem

(log_)(21)−(log_)(3)

Solution

1. Identify the logarithmic property for subtraction, which is the Quotient Rule: (log_b)(M)−(log_b)(N)=(log_b)(M/N)

2. Apply the rule by rewriting the difference of the two logarithms as the logarithm of a single fraction.

(log_)(21)−(log_)(3)=(log_)(21/3)

3. Simplify the fraction inside the logarithm by dividing 21 by 3.

21/3=7

Final Answer

(log_)(21)−(log_)(3)=(log_)(7)

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