Evaluate ( log of 13)/( log of 5)

Problem

(log_)(13)/(log_)(5)

Solution

1. Identify the expression as a ratio of logarithms with the same base (implied base 10 or base 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 5 and argument 13.

4. Calculate the numerical value using a calculator if a decimal approximation is required.

Final Answer

(log_)(13)/(log_)(5)=(log_5)(13)≈1.5937

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