Expand the Logarithmic Expression log of zy^7

Problem

(log_)(z*y^7)

Solution

1. Identify the product inside the logarithm, which consists of the variables z and y^7

2. Apply the product rule for logarithms, which states that (log_)(a*b)=(log_)(a)+(log_)(b)

(log_)(z*y^7)=(log_)(z)+(log_)(y^7)

3. Apply the power rule for logarithms to the second term, which states that (log_)(a^n)=n*(log_)(a)

(log_)(y^7)=7*(log_)(y)

4. Combine the results to write the fully expanded expression.

(log_)(z)+7*(log_)(y)

Final Answer

(log_)(z*y^7)=(log_)(z)+7*(log_)(y)

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