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

asked Sep 14, 2021 60.7k views

5 votes

Given

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

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

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4 votes

Explanation:

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

then for y:

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

so:

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