Evaluate log base 12 of 2

Problem

(log_12)(2)

Solution

1. Apply the change of base formula to rewrite the expression using common logarithms (base 10) or natural logarithms (base e.

2. Substitute the formula (log_b)(a)=ln(a)/ln(b)

3. Calculate the values of the logarithms using a calculator.

ln(2)≈0.693147

4. Calculate the value of the denominator.

ln(12)≈2.484907

5. Divide the two values to find the final decimal approximation.

0.693147/2.484907≈0.278943

Final Answer

(log_12)(2)≈0.278943

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