Simplify/Condense log base 2 of 16- log base 2 of 8

Problem

(log_2)(16)−(log_2)(8)

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 quotient rule to combine the two terms into a single logarithm.

(log_2)(16)−(log_2)(8)=(log_2)(16/8)

3. Simplify the fraction inside the logarithm.

(log_2)(16/8)=(log_2)(2)

4. Evaluate the resulting logarithm by determining the power to which the base 2 must be raised to equal 2

(log_2)(2)=1

Final Answer

(log_2)(16)−(log_2)(8)=1

Want more problems? Check here!