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

Problem

(log_)(x)−2*(log_)(y)+3*(log_)(z)

Solution

1. Apply the Power Property of logarithms, which states n*(log_)(a)=(log_)(an) to the terms with coefficients.

(log_)(x)−(log_)(y2)+(log_)(z3)

2. Apply the Quotient Property of logarithms, which states (log_)(a)−(log_)(b)=(log_)(a/b) to the first two terms.

(log_)(x/(y2))+(log_)(z3)

3. Apply the Product Property of logarithms, which states (log_)(a)+(log_)(b)=(log_)(a*b) to combine the remaining terms.

(log_)((x⋅z3)/(y2))

Final Answer

(log_)(x)−2*(log_)(y)+3*(log_)(z)=(log_)((x*z3)/(y2))

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