Mathematics - Sequence & Series Question with Solution | TestHub

Given${\log }_{\left(7^{1/2}\right)}x+{\log }_{\left(7^{1/3}\right)}x+{\log }_{\left(7^{1/4}\right)}x+\dots 20$times$=460$
$\Rightarrow (2+3+4+\dots ..+21){\log }_{7}x=460$
$\Rightarrow \frac{20}{2}(2+21){\log }_{7}x=460$
$\Rightarrow {\log }_{7}x=2$
$\Rightarrow x=49$