Evaluate log base 4 of 97

Problem

(log_4)(97)

Solution

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

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

2. Substitute the given values a=97 and b=4 into the formula.

(log_4)(97)=ln(97)/ln(4)

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

ln(97)≈4.5747109785

ln(4)≈1.3862943611

4. Divide the results to find the decimal approximation.

4.5747109785/1.3862943611≈3.3000285

Final Answer

(log_4)(97)≈3.3000285

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