Question

expressions using properties
submitting an external tool
f - base formula to evaluate the following expression, round to 4 decimal places if necessary:
$\log_5 62$

Explanation:

Step1: Apply change - of - base formula

The change - of - base formula is \(\log_{a}b=\frac{\ln b}{\ln a}\) or \(\log_{a}b = \frac{\log_{10}b}{\log_{10}a}\). For \(\log_{5}62\), using \(\log_{a}b=\frac{\ln b}{\ln a}\), we have \(\log_{5}62=\frac{\ln62}{\ln5}\).

Step2: Calculate the natural logarithms

We know that \(\ln62\approx4.127134\) and \(\ln5\approx1.609438\).

Step3: Divide the values

\(\frac{\ln62}{\ln5}=\frac{4.127134}{1.609438}\approx2.564949\)

Answer:

\(2.5649\)