Evaluate log base 4 of 7

Problem

(log_4)(7)

Solution

1. Identify the expression as a logarithm with base 4 and argument 7.

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

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

4. Calculate the numerical value using the natural logarithms of 7 and 4.

5. Simplify the result to a decimal approximation.

Final Answer

(log_4)(7)≈1.4037

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