Evaluate log base 3 of 20

Problem

(log_3)(20)

Solution

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

(log_b)(a)=ln(a)/ln(b)

2. Substitute the given values into the formula.

(log_3)(20)=ln(20)/ln(3)

3. Calculate the values of the natural logarithms.

ln(20)≈2.99573

ln(3)≈1.09861

4. Divide the results to find the decimal approximation.

2.99573/1.09861≈2.72683

Final Answer

(log_3)(20)≈2.7268

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