how does the value of $log_2{100}$ compare with the value of $log_6{20}$?\nthe value of $log_2{100}$ is…

Explanation:

Step1: Use change - of - base formula

The change - of - base formula is $\log_a b=\frac{\ln b}{\ln a}$. So, $\log_2 100=\frac{\ln 100}{\ln 2}$ and $\log_6 20=\frac{\ln 20}{\ln 6}$.

Step2: Calculate the values

$\log_2 100=\frac{\ln 100}{\ln 2}\approx\frac{4.6052}{0.6931}\approx6.64$. $\log_6 20=\frac{\ln 20}{\ln 6}\approx\frac{2.9957}{1.7918}\approx1.67$.

Step3: Find the ratio

$\frac{\log_2 100}{\log_6 20}\approx\frac{6.64}{1.67} = 4$.

Answer:

The value of $\log_2 100$ is about 4 times the value of $\log_6 20$.