Answer:
[tex]\large\boxed{\sf n^2 \ log \ x }[/tex]
Step-by-step explanation:
Given that ,
[tex]\longrightarrow \log \ x + \log\ x^3 + \log \ x^5\ \dots + \log x^{2n-1} [/tex]
As we know that , [tex] \log x^n = n \log x [/tex] , therefore ;
[tex]\longrightarrow \log x + 3\log x + 5\log_x +\dots + (2n-1)\log x [/tex]
Take out log x as common ;
[tex]\longrightarrow \log x ( 1 + 3+5+...+(2n-1))[/tex]
The terms inside the brackets are the sum of first n odd numbers . And we know that the sum of first n odd numbers in n² . Therefore ;
[tex]\longrightarrow \log x (n^2) \\[/tex]
[tex]\longrightarrow \underline{\underline{\red{{ n^2\log x }}}}[/tex]
Option c is correct!
