obtain an approximate value for the logarithm using natural logarithms.\n\\log_{25}60\n\\log_{25}60\\approx\\…

Explanation:

Step1: Recall Change of Base Formula

The change of base formula for logarithms is $\log_{b}a = \frac{\ln a}{\ln b}$, where $\ln$ is the natural logarithm. Here, $b = 25$ and $a = 60$.

Step2: Calculate Natural Logarithms

First, find $\ln 60$ and $\ln 25$. Using a calculator, $\ln 60 \approx 4.094344562$, and $\ln 25 \approx 3.218875825$.

Step3: Divide the Logarithms

Now, divide $\ln 60$ by $\ln 25$: $\frac{\ln 60}{\ln 25} \approx \frac{4.094344562}{3.218875825} \approx 1.271$.

Answer:

1.271