Lakshyamanchester wrote:
If (5.55)^x = (0.555)^y = 1000, then the value of 1/x - 1/y is?
A) 1/3
B) 1
C) 2/3
D) 2
E) 3
Key concept: \((b^n)^{\frac{1}{n}} = b\)Take: \(5.55^x = 1000\)
Raise both sides to the power of \(\frac{1}{x}\) to get: \(5.55 = 1000^{\frac{1}{x}}\)
Take: \(0.555^y = 1000\)
Raise both sides to the power of \(\frac{1}{y}\) to get: \(0.555 = 1000^{\frac{1}{y}}\)
This means: \(\frac{5.55}{0.555}= \frac{1000^{\frac{1}{x}}}{1000^{\frac{1}{y}}}\)
Simplify both sides: \(10= 1000^{\frac{1}{x} - \frac{1}{y}}\)
Rewrite 1000 as follows: \(10= (10^3)^{\frac{1}{x} - \frac{1}{y}}\)
Simplify: \(10^1= 10^{3(\frac{1}{x} - \frac{1}{y})}\)
This means: \(1 = 3(\frac{1}{x} - \frac{1}{y})\)
Divide both sides by 3 to get: \(\frac{1}{3} = \frac{1}{x} - \frac{1}{y}\)
Answer: A
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