Simplify/Condense

Problem

(log_8)(6)−(log_8)(3)+(log_8)(2)

Solution

1. Apply the Quotient Rule for logarithms to the first two terms, which states (log_b)(M)−(log_b)(N)=(log_b)(M/N)

(log_8)(6)−(log_8)(3)=(log_8)(6/3)

2. Simplify the fraction inside the logarithm.

(log_8)(2)+(log_8)(2)

3. Apply the Product Rule for logarithms, which states (log_b)(M)+(log_b)(N)=(log_b)(M⋅N)

(log_8)(2⋅2)=(log_8)(4)

4. Evaluate the logarithm by expressing the base and the argument as powers of the same base, 2

(log_2)(2)

5. Apply the Change of Base formula or the property (log_bn)(am)=m/n*(log_b)(a)

2/3*(log_2)(2)

6. Simplify using the identity (log_b)(b)=1

2/3⋅1=2/3

Final Answer

(log_8)(6)−(log_8)(3)+(log_8)(2)=2/3

Want more problems? Check here!