Expand the Logarithmic Expression log base 2 of AB^2

Problem

(log_2)(A*B2)

Solution

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

(log_2)(A*B2)=(log_2)(A)+(log_2)(B2)

2. Apply the power rule for logarithms, which states that (log_b)(xp)=p*(log_b)(x) to the second term.

(log_2)(B2)=2*(log_2)(B)

3. Combine the terms to write the fully expanded expression.

(log_2)(A)+2*(log_2)(B)

Final Answer

(log_2)(A*B2)=(log_2)(A)+2*(log_2)(B)

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