Simplify/Condense log base 6 of 36x^3

Problem

(log_6)(36*x3)

Solution

1. Identify the expression as a single logarithm containing a product of two terms, 36 and x3

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

(log_6)(36*x3)=(log_6)(36)+(log_6)(x3)

3. Evaluate the first term by recognizing that 36=6 so (log_6)(6)=2

(log_6)(36)=2

4. Apply the power rule for logarithms to the second term, which states (log_b)(Mp)=p*(log_b)(M)

(log_6)(x3)=3*(log_6)(x)

5. Combine the simplified parts into the final expression.

2+3*(log_6)(x)

Final Answer

(log_6)(36*x3)=2+3*(log_6)(x)

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