Question

obtain an approximate value for the logarithm using natural logarithms. \\(\log_{24} 91\\) \\(\log_{24} 91 \approx \square\\) (round to three decimal places as needed.)

Explanation:

Step1: Recall Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\ln a}{\ln b}$, where $\ln$ denotes the natural logarithm. Here, $b = 24$ and $a = 91$.

Step2: Calculate Natural Logarithms

First, find $\ln 91$ and $\ln 24$. Using a calculator, $\ln 91 \approx 4.510859$ and $\ln 24 \approx 3.178054$.

Step3: Divide the Logarithms

Now, divide $\ln 91$ by $\ln 24$: $\frac{\ln 91}{\ln 24} \approx \frac{4.510859}{3.178054} \approx 1.420$.

Answer:

1.420