Evaluate ( log of 42)/( log of 7)

Problem

(log_)(42)/(log_)(7)

Solution

1. Identify the expression as a ratio of logarithms with the same base (implied base 10 or e.

2. Apply the change of base formula, which states that (log_b)(a)/(log_b)(c)=(log_c)(a)

3. Rewrite the expression as a single logarithm with base 7.

4. Factor the argument 42 into 7×6 to simplify further if needed.

5. Apply the product rule for logarithms, (log_b)(x*y)=(log_b)(x)+(log_b)(y)

6. Simplify the term (log_7)(7) to 1.

Final Answer

(log_)(42)/(log_)(7)=1+(log_7)(6)

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