Evaluate log base 7 of 2506

Problem

(log_7)(2506)

Solution

1. Apply the change of base formula to rewrite the expression using natural logarithms or common logarithms.

(log_7)(2506)=ln(2506)/ln(7)

2. Calculate the natural logarithm of the numerator and the denominator.

ln(2506)≈7.82644

ln(7)≈1.94591

3. Divide the two values to find the numerical approximation.

7.82644/1.94591≈4.02200

Final Answer

(log_7)(2506)≈4.022

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