Question

use the change of base formula to compute \\(\log_{4} 3\\).
round your answer to the nearest thousandth.

Explanation:

Step1: Recall change of base formula

The change of base formula for logarithms is \(\log_{b}a=\frac{\log_{c}a}{\log_{c}b}\), where \(c > 0,c
eq1\). We can use \(c = 10\) (common logarithm) or \(c=e\) (natural logarithm). Let's use common logarithm (base 10) here. So for \(\log_{4}3\), we have \(\log_{4}3=\frac{\log_{10}3}{\log_{10}4}\).

Step2: Calculate the logarithms

We know that \(\log_{10}3\approx0.4771\) and \(\log_{10}4\approx0.6021\).

Step3: Divide the two values

Now, we divide \(\log_{10}3\) by \(\log_{10}4\): \(\frac{0.4771}{0.6021}\approx0.792\) (rounded to the nearest thousandth).

Answer:

\(0.792\)