Evaluate log base 6 of 18- log base 6 of 3

Problem

(log_6)(18)−(log_6)(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 to the given expression by dividing the arguments of the logarithms.

(log_6)(18)−(log_6)(3)=(log_6)(18/3)

3. Simplify the fraction inside the logarithm.

18/3=6

4. Evaluate the resulting logarithm by determining the power to which the base 6 must be raised to equal 6

(log_6)(6)=1

Final Answer

(log_6)(18)−(log_6)(3)=1

Want more problems? Check here!