Simplify/Condense 2 log of x+3 log of y-6 log of z

Problem

2*(log_)(x)+3*(log_)(y)−6*(log_)(z)

Solution

1. Apply the Power Property of logarithms, which states n*(log_)(a)=(log_)(an) to each term in the expression.

(log_)(x2)+(log_)(y3)−(log_)(z6)

2. Apply the Product Property of logarithms, which states (log_)(a)+(log_)(b)=(log_)(a*b) to the first two terms.

(log_)(x2*y3)−(log_)(z6)

3. Apply the Quotient Property of logarithms, which states (log_)(a)−(log_)(b)=(log_)(a/b) to combine the remaining terms into a single logarithm.

(log_)((x2*y3)/(z6))

Final Answer

2*(log_)(x)+3*(log_)(y)−6*(log_)(z)=(log_)((x2*y3)/(z6))

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