Evaluate log base 3 of 7

Problem

(log_3)(7)

Solution

1. Identify the expression as a logarithm with base 3 and argument 7.

2. Apply the change of base formula to convert the expression into a form that can be calculated using common logarithms (base 10) or natural logarithms (base e.

3. Use the formula (log_b)(a)=ln(a)/ln(b)

4. Substitute the values into the formula to get ln(7)/ln(3)

5. Calculate the numerical value using the approximate values ln(7)≈1.9459 and ln(3)≈1.0986

Final Answer

(log_3)(7)=ln(7)/ln(3)≈1.7712

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