Evaluate log base 2 of 17

Problem

(log_2)(17)

Solution

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

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

2. Substitute the values from the original expression into the formula, where a=17 and b=2

(log_2)(17)=ln(17)/ln(2)

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

ln(17)≈2.833213

ln(2)≈0.693147

4. Divide the results to find the final decimal approximation.

2.833213/0.693147≈4.087463

Final Answer

(log_2)(17)≈4.087463

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