Expand the Logarithmic Expression log of (xy)/z

Problem

(log_)((x*y)/z)

Solution

1. Apply the quotient rule for logarithms, which states that (log_)(A/B)=(log_)(A)−(log_)(B)

(log_)((x*y)/z)=(log_)(x*y)−(log_)(z)

2. Apply the product rule for logarithms to the first term, which states that (log_)(A*B)=(log_)(A)+(log_)(B)

(log_)(x*y)−(log_)(z)=(log_)(x)+(log_)(y)−(log_)(z)

Final Answer

(log_)((x*y)/z)=(log_)(x)+(log_)(y)−(log_)(z)

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