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Re: If (5.55)^x = (0.555)^y = 1000, then the value of 1/x - 1/y is? [#permalink]
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


Explanation:

Given: (5.55)^x = (0.555)^y = 1000 =10^3

Taking log with respect to 10 ( that is base 10)

x log 5.55 = y log (0.555) = 3 log 10 = 3

x log 5.55 = 3
x = 3/log5.55
1/x = log 5.55/3 ---1

y log (0.555) = 3
y log (5.55/10) = 3
y log 5.55 – y log 10 = 3
y log 5.55 – y = 3
y = 3 /(log 5.55 -1)
1/y = (log 5.55 -1)/3 ---2

From equation 1 & 2

1/x -1/y = 1/3
IMO-A
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Re: If (5.55)^x = (0.555)^y = 1000, then the value of 1/x - 1/y is? [#permalink]
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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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Re: If (5.55)^x = (0.555)^y = 1000, then the value of 1/x - 1/y is? [#permalink]
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Re: If (5.55)^x = (0.555)^y = 1000, then the value of 1/x - 1/y is? [#permalink]
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