Simplify/Condense log of 9- log of 3

Problem

(log_)(9)−(log_)(3)

Solution

1. Identify the logarithmic property for subtraction, which is the Quotient Rule for Logarithms.

2. Apply the formula (log_b)(M)−(log_b)(N)=(log_b)(M/N) to the given expression.

3. Substitute the values M=9 and N=3 into the quotient.

(log_)(9)−(log_)(3)=(log_)(9/3)

4. Simplify the fraction inside the logarithm by dividing 9 by 3.

(log_)(9/3)=(log_)(3)

Final Answer

(log_)(9)−(log_)(3)=(log_)(3)

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