Expand the Logarithmic Expression log base a of 4x^3y

Problem

(log_a)(4*x3*y)

Solution

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

(log_a)(4⋅x3⋅y)=(log_a)(4)+(log_a)(x3)+(log_a)(y)

2. Apply the power rule for logarithms to the term (log_a)(x3) which states that (log_b)(Mp)=p*(log_b)(M)

(log_a)(x3)=3*(log_a)(x)

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

(log_a)(4)+3*(log_a)(x)+(log_a)(y)

Final Answer

(log_a)(4*x3*y)=(log_a)(4)+3*(log_a)(x)+(log_a)(y)

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