Evaluate log base 6 of 11*13

Problem

(log_6)(11⋅13)

Solution

1. Identify the expression as a logarithm of a product.

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

3. Expand the expression using the rule.

4. Simplify the product inside the logarithm if the task requires a single numerical argument, or leave it expanded if the task requires logarithmic properties. Since the task asks to evaluate, we first multiply the numbers.

5. Calculate the product of the arguments.

11⋅13=143

6. Rewrite the expression in its simplest logarithmic form.

Final Answer

(log_6)(11⋅13)=(log_6)(143)

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