Expand the Logarithmic Expression log base 8 of (xy)^10

Problem

(log_8)((x*y)10)

Solution

1. Apply the power rule for logarithms, which states that (log_b)(an)=n*(log_b)(a)

(log_8)((x*y)10)=10*(log_8)(x*y)

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

10*(log_8)(x*y)=10*((log_8)(x)+(log_8)(y))

3. Distribute the constant factor to both terms inside the parentheses.

10*((log_8)(x)+(log_8)(y))=10*(log_8)(x)+10*(log_8)(y)

Final Answer

(log_8)((x*y)10)=10*(log_8)(x)+10*(log_8)(y)

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