Mathematics

Problem

If the sum of the first 20 terms of the series

\log_{(7^{1/2})} x + \log_{(7^{1/3})} x + \log_{(7^{1/4})} x + \dots

is 460, then

x

is equal to (a)

7^2

(b)

7^{1/2}

(c)

e^2

(d)

7^{46/21}