Evaluate log base 2 of 3

Problem

(log_2)(3)

Solution

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

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

2. Substitute the values a=3 and b=2 into the formula.

(log_2)(3)=ln(3)/ln(2)

3. Calculate the approximate values of the natural logarithms.

ln(3)≈1.098612

ln(2)≈0.693147

4. Divide the results to find the decimal approximation.

1.098612/0.693147≈1.584963

Final Answer

(log_2)(3)≈1.584963

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