devonte used the change of base formula to approximate $log_{8}25$. which expression did devonte…

devonte used the change of base formula to approximate $log_{8}25$. which expression did devonte use?\n$log\frac{8}{25}$\n$\frac{log8}{log25}$\n$log\frac{25}{8}$\n$\frac{log25}{log8}$

devonte used the change of base formula to approximate $log_{8}25$. which expression did devonte use?\n$log\frac{8}{25}$\n$\frac{log8}{log25}$\n$log\frac{25}{8}$\n$\frac{log25}{log8}$

Answer

Explanation:

Step1: Recall change - of - base formula

The change - of - base formula for logarithms is $\log_{a}b=\frac{\log_{c}b}{\log_{c}a}$, where $c$ can be any positive number other than 1. Commonly, $c = 10$ (common logarithm) or $c=e$ (natural logarithm). For $\log_{8}25$, using the change - of - base formula with common logarithm ($c = 10$), we have $\log_{8}25=\frac{\log25}{\log8}$.

Answer:

$\frac{\log25}{\log8}$ (the fourth option)