Given log(x) = 2 \: and \: log(y) = - 1 prove that xy - 100y {}^(2) = 9 ​

Question

Given


`log(x) = 2 \: and \: log(y) = - 1`
prove that

`xy - 100y {}^(2) = 9`

​

Answer 1

Explanation:

`log(x) = 2 \\ {10}^(2) = x \\ x = 100`

then for y:

`log( y) = - 1 \\ {10}^( - 1) = y \\ y = 0.1`

so:

`xy - 100 {y}^(2) \\ = 100 * 0.1 - 100 * {(0.1)}^(2) \\ = 10 - 100 * 0.01 \\ = 10 - 1 \\ = 9`