Question

Chapter - logarithms

Please help!!!​

Answer 1

`\large\boxed{\sf n^2 \ log \ x }`

Explanation:

Given that ,

`\longrightarrow \log \ x + \log\ x^3 + \log \ x^5\ \dots + \log x^(2n-1)`

As we know that ,
`\log x^n = n \log x` , therefore ;

`\longrightarrow \log x + 3\log x + 5\log_x +\dots + (2n-1)\log x`

Take out log x as common ;

`\longrightarrow \log x ( 1 + 3+5+...+(2n-1))`

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 ;

`\longrightarrow \log x (n^2) \\`

`\longrightarrow \underline{\underline{\red{{ n^2\log x }}}}`

Option c is correct!