Expand the Logarithmic Expression -4 log base 6 of 2x

Problem

−4*(log_6)(2*x)

Solution

1. Identify the logarithmic property for products, which states (log_b)(M*N)=(log_b)(M)+(log_b)(N)

2. Apply the product rule to the expression inside the logarithm, treating 2 and x as the factors.

−4*((log_6)(2)+(log_6)(x))

3. Distribute the constant −4 to both terms inside the parentheses.

−4*(log_6)(2)−4*(log_6)(x)

Final Answer

−4*(log_6)(2*x)=−4*(log_6)(2)−4*(log_6)(x)

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