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

evaluate the expression.\\(\\log_{4} 316\\)\\(\\log_{4} 316 = \\square\\)\\(\\text{(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\\)\\(\\text{(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 logarithms

$\ln 316 \approx 5.756213$, $\ln 4 \approx 1.386294$

Step3: Divide the two values

$\frac{5.756213}{1.386294} \approx 4.152198$

Answer:

4.152198