Simplify/Condense log base 5 of 250- log base 5 of 2

Problem

(log_5)(250)−(log_5)(2)

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 formula by combining the two logarithms into a single logarithm with the arguments in a fraction.

(log_5)(250)−(log_5)(2)=(log_5)(250/2)

3. Simplify the fraction inside the logarithm by dividing 250 by 2.

(log_5)(250/2)=(log_5)(125)

4. Evaluate the logarithm by expressing 125 as a power of the base 5, noting that 125=5

(log_5)(5)=3

Final Answer

(log_5)(250)−(log_5)(2)=3

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