Evaluate ( natural log of 4)/( natural log of 3)

Problem

ln(4)/ln(3)

Solution

1. Identify the expression as a ratio of two natural logarithms.

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

3. Rewrite the expression using the base of the denominator.

4. Simplify the numerator if possible by noting that 4=2 allowing the expression to be written as (2*ln(2))/ln(3)

5. Calculate the numerical value using the approximations ln(4)≈1.3863 and ln(3)≈1.0986

Final Answer

ln(4)/ln(3)=(log_3)(4)≈1.2619

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