If log 2 = 0.3010 and log 3 = 0.4771, What is the value of $log_{5}1024$?
4.31
3.88
3.91
2.97
Explanation:
$log_{5}1024$
$\dfrac{log\:1024}{log\:5}$
=$\dfrac{log\left(2^{10}\right)}{log\left(\dfrac{10}{2}\right)}$
=$\dfrac{10\:log\left(2\right)}{log\:10-log\:2}$
=$\dfrac{10\times0.3010}{1-0.3010}$
=$\dfrac{3.01}{0.699}$
=$\dfrac{3010}{699}$
=4.31