Expand the Logarithmic Expression log base 2 of (ab)^2

Problem

(log_2)((a*b)2)

Solution

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

(log_2)((a*b)2)=2*(log_2)(a*b)

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

2*(log_2)(a*b)=2*((log_2)(a)+(log_2)(b))

3. Distribute the constant factor to each term inside the parentheses.

2*((log_2)(a)+(log_2)(b))=2*(log_2)(a)+2*(log_2)(b)

Final Answer

(log_2)((a*b)2)=2*(log_2)(a)+2*(log_2)(b)

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