Expand the Logarithmic Expression log of 100x^3y^5

Problem

(log_)(100*x3*y5)

Solution

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

(log_)(100)+(log_)(x3)+(log_)(y5)

2. Evaluate the constant term by recognizing that (log_)(100) is the common logarithm (base 10) of 10

2+(log_)(x3)+(log_)(y5)

3. Apply the power rule for logarithms, which states that (log_)(an)=n*(log_)(a) to the remaining terms.

2+3*(log_)(x)+5*(log_)(y)

Final Answer

(log_)(100*x3*y5)=2+3*(log_)(x)+5*(log_)(y)

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