Indices problem 3 by Dhaval Furia

Algebra Level pending

If $(5.55)^{x} = (0.555)^{y} = 1000$ , then the value of $\frac {1}{x} - \frac {1}{y}$ is $_____$

\frac {1}{3}

\frac {2}{3}

3

1

1 solution

Tom Engelsman
Jul 30, 2020

Knowing that $(\frac{555}{100})^{x} = 10^3 = (\frac{555}{1000})^{y} \Rightarrow 10^3 = (\frac{555}{100} \cdot \frac{1}{10})^y = (10^{3/x - 1})^y$ , equating both exponents yields:

$3 = \frac{3y}{x} - y \Rightarrow \frac{3}{y} = \frac{3}{x} - 1 \Rightarrow \frac{3}{x} - \frac{3}{y} = 1 \Rightarrow \boxed{\frac{1}{x} - \frac{1}{y} = \frac{1}{3}}.$

Indices problem 3 by Dhaval Furia

1 solution

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