Simplify/Condense log of 14+1/2* log of 3- log of 2

Problem

(log_)(14)+1/2*(log_)(3)−(log_)(2)

Solution

1. Apply the power property of logarithms, which states n*(log_)(b)=(log_)(bn) to the second term.

1/2*(log_)(3)=(log_)(3(1/2))

(log_)(3(1/2))=(log_)(√(,3))

2. Apply the product property of logarithms, (log_)(a)+(log_)(b)=(log_)(a*b) to the first two terms.

(log_)(14)+(log_)(√(,3))=(log_)(14√(,3))

3. Apply the quotient property of logarithms, (log_)(a)−(log_)(b)=(log_)(a/b) to the remaining expression.

(log_)(14√(,3))−(log_)(2)=(log_)((14√(,3))/2)

4. Simplify the fraction inside the logarithm by dividing the coefficients.

(14√(,3))/2=7√(,3)

Final Answer

(log_)(14)+1/2*(log_)(3)−(log_)(2)=(log_)(7√(,3))

Want more problems? Check here!