Question

if
${2.3}^{x} = {0.23}^{y} = 1000$
then find the value of
$\frac{1}{x} - \frac{1}{y}$



​

Answer 1

$HEYA \: \\ \\ (2.3) {}^{x} = (0.23) {}^{y} = 10 {}^{3} = k \: \: (let) \\ \\ (2.3) {}^{x} = k \: \: \ \: \: (0.23) {}^{y} = k \: \: \: \: \: k = 10 {}^{3} \\ \\ k {}^{(1 \div x)} = 2.3 \: \: \: \: \: ...i \\ \\ k {}^{(1 \div y)} = (0.23) \: \: \: \: ...ii \\ and \\ k {}^{(1 \div 3)} = 10 \: \: ...iii \\ \\ divide \: i \: by \: ii \: we \: \: have \\ \\ k {}^{(1 \div x) - (1 \div y)} = (2.3) \div (0.23) \\ \\ k {}^{(1 \div x) - (1 \div y)} = 10 \\ \\ from \: iii \: we \: have \\ \\ k {}^{(1 \div x) - (1 \div y)} = k {}^{(1 \div 3)} \\ \\ now \: compare \: powers \: of \: k \: we \: get \\ \\ (1 \div x) - (1 \div y) = (1 \div 3 )\\ \\ therefore \: \: \: \: \: (1 \div x) - (1 \div y) = (1 \div 3)$