Expand the Logarithmic Expression log of (6x^5y^3)/(7z^2)

Problem

(log_)((6*x5*y3)/(7*z2))

Solution

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

(log_)(6*x5*y3)−(log_)(7*z2)

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

(log_)(6)+(log_)(x5)+(log_)(y3)−((log_)(7)+(log_)(z2))

3. Distribute the negative sign through the second set of parentheses.

(log_)(6)+(log_)(x5)+(log_)(y3)−(log_)(7)−(log_)(z2)

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

(log_)(6)+5*(log_)(x)+3*(log_)(y)−(log_)(7)−2*(log_)(z)

Final Answer

(log_)((6*x5*y3)/(7*z2))=(log_)(6)+5*(log_)(x)+3*(log_)(y)−(log_)(7)−2*(log_)(z)

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