Evaluate ( log of 6)/( log of 5)

Problem

(log_)(6)/(log_)(5)

Solution

1. Identify the expression as a ratio of logarithms with an implicit base, typically base 10 or base e

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

3. Rewrite the expression using the formula where a=5 and x=6

4. Calculate the numerical value if a decimal approximation is required, using (log_)(6)≈0.77815 and (log_)(5)≈0.69897

5. Divide the values to find the approximate result.

Final Answer

(log_)(6)/(log_)(5)=(log_5)(6)≈1.1133

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