Expand the Logarithmic Expression log of (x^3y^4)/(z^6)

Problem

(log_)((x3*y4)/(z6))

Solution

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

(log_)(x3*y4)−(log_)(z6)

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

(log_)(x3)+(log_)(y4)−(log_)(z6)

3. Apply the power rule for logarithms, which states that (log_)(Ap)=p*(log_)(A) to each term.

3*(log_)(x)+4*(log_)(y)−6*(log_)(z)

Final Answer

(log_)((x3*y4)/(z6))=3*(log_)(x)+4*(log_)(y)−6*(log_)(z)

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