Evaluate log base 2 of 7

Problem

(log_2)(7)

Solution

1. Identify the expression as a logarithm with base 2 and argument 7.

2. Apply the change of base formula to convert the expression into a form that can be calculated using common logarithms (base 10) or natural logarithms (base e.

3. Use the formula (log_b)(a)=ln(a)/ln(b)

4. Substitute the values into the formula.

(log_2)(7)=ln(7)/ln(2)

5. Calculate the numerical values using a calculator for an approximate decimal result.

ln(7)≈1.94591

ln(2)≈0.69315

1.94591/0.69315≈2.80735

Final Answer

(log_2)(7)=ln(7)/ln(2)≈2.80735

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