approximate: $log_{5}\frac{4}{7}$\n-2.8760\n-0.3477\n0.7124\n1.3738\ndone

Explanation:

Step1: Use logarithm quotient - rule

$\log_{a}\frac{M}{N}=\log_{a}M - \log_{a}N$. So, $\log_{5}\frac{4}{7}=\log_{5}4-\log_{5}7$.

Step2: Use change - of - base formula

The change - of - base formula is $\log_{a}b=\frac{\ln b}{\ln a}$. Then $\log_{5}4 = \frac{\ln4}{\ln5}\approx\frac{1.3863}{1.6094}\approx0.8614$ and $\log_{5}7=\frac{\ln7}{\ln5}\approx\frac{1.9459}{1.6094}\approx1.2083$.

Step3: Calculate the result

$\log_{5}\frac{4}{7}=\log_{5}4-\log_{5}7\approx0.8614 - 1.2083=- 0.3469\approx - 0.3477$.

Answer:

-0.3477