Expand the Logarithmic Expression log of (x^2y)/(z^3)

Problem

(log_)((x2*y)/(z3))

Solution

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

(log_)((x2*y)/(z3))=(log_)(x2*y)−(log_)(z3)

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

(log_)(x2*y)−(log_)(z3)=(log_)(x2)+(log_)(y)−(log_)(z3)

3. Apply the power rule for logarithms, which states (log_)(An)=n*(log_)(A) to the terms with exponents.

(log_)(x2)+(log_)(y)−(log_)(z3)=2*(log_)(x)+(log_)(y)−3*(log_)(z)

Final Answer

(log_)((x2*y)/(z3))=2*(log_)(x)+(log_)(y)−3*(log_)(z)

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