QUESTION 13 - 1 POINT
Use the change of base formula to express $\log _{2} 6$ using $\ln$, the natural logarithm (log base $e$ ).
Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta keyboard.
Provide your answer below:
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Answer
Final Answer: \(\boxed{2.584962500721156}\)
Step 1 ：The change of base formula is given by \(\log_b a = \frac{\log_c a}{\log_c b}\) for any positive base \(c\) different from 1. In this case, we want to express \(\log_2 6\) using \(\ln\), so we can take \(c = e\). Therefore, we have \(\log_2 6 = \frac{\ln 6}{\ln 2}\).
Step 2 ：After calculating, we get the result as 2.584962500721156.
Step 3 ：Final Answer: \(\boxed{2.584962500721156}\)
