Simplify/Condense log base 6 of 864- log base 6 of 4

Problem

(log_6)(864)−(log_6)(4)

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

(log_6)(864/4)

3. Divide the numbers inside the logarithm to simplify the argument.

864/4=216

4. Rewrite the expression with the simplified argument.

(log_6)(216)

5. Evaluate the logarithm by expressing 216 as a power of the base 6. Since 6^3=216 the value is 3.

(log_6)(6^3)=3

Final Answer

(log_6)(864)−(log_6)(4)=3

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