Simplify/Condense log of x+7 log of y

Problem

(log_)(x)+7*(log_)(y)

Solution

1. Identify the logarithmic properties needed to condense the expression, specifically the Power Property and the Product Property.

2. Apply the Power Property of logarithms, which states n*(log_)(a)=(log_)(an) to the second term.

(log_)(x)+(log_)(y7)

3. Apply the Product Property of logarithms, which states (log_)(a)+(log_)(b)=(log_)(a*b) to combine the two terms into a single logarithm.

(log_)(x⋅y7)

Final Answer

(log_)(x)+7*(log_)(y)=(log_)(x*y7)

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