evaluate the expression. \\(\\log_{4} 316\\) \\(\\log_{4} 316 = \\square\\) (simplify your answer. type an…

evaluate the expression. \\(\\log_{4} 316\\) \\(\\log_{4} 316 = \\square\\) (simplify your answer. type an integer or decimal rounded to six decimal places as needed.)

evaluate the expression. \\(\\log_{4} 316\\) \\(\\log_{4} 316 = \\square\\) (simplify your answer. type an integer or decimal rounded to six decimal places as needed.)

Answer

Explanation:

Step1: Apply change of base formula

$\log_{4}316 = \frac{\ln 316}{\ln 4}$

Step2: Calculate natural logs

$\ln 316 \approx 5.756203$, $\ln 4 \approx 1.386294$

Step3: Divide the two values

$\frac{5.756203}{1.386294} \approx 4.152168$

Answer:

4.152168