Evaluate log base 3 of 14

Problem

(log_3)(14)

Solution

1. Identify the expression as a logarithm with base 3 and argument 14

2. Apply the change of base formula to convert the expression into a form that can be calculated using standard logarithms, such as the natural logarithm ln() or common logarithm (log_10)()

3. Substitute the values into the formula (log_b)(a)=ln(a)/ln(b)

4. Calculate the numerical value using the natural logarithms of 14 and 3

5. Simplify the result to a decimal approximation.

Final Answer

(log_3)(14)≈2.40217

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