Question:
If (5.55) x (0.555)y = 1000, then the value of 1/x - 1/y is
If (5.55) x (0.555)y = 1000, then the value of 1/x - 1/y is
Updated On: Aug 21, 2024
- 3
- 1
- 1/3
- 2/3
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The Correct Option is C
Solution and Explanation
Given that
(5.55)x = 1000
(5.55)x = 10³
By Taking log both the side we get
xlog10 ( 5.55 ) = 3
⇒ log10 ( 5.55 ) = \(\frac{3}{x}\)
⇒ log10 ( 10 × 0.555 ) = \(\frac{3}{x}\)
⇒ log10 ( 0.555 ) + 1 = \(\frac{3}{x}\) ..... (1)
Also, we have
(0.555)y = 1000
Taking log both the side
y log10 ( 0.555 ) = 3
⇒ log10 ( 5.55 ) = \(\frac{3}{x}\) ..... (2)
From equation (1) and (2), we get
\(\frac{3}{y}+1=\frac{3}{x}\)
⇒ \(\frac{1}{x}-\frac{1}{y}=\frac{1}{3}\)
(5.55)x = 1000
(5.55)x = 10³
By Taking log both the side we get
xlog10 ( 5.55 ) = 3
⇒ log10 ( 5.55 ) = \(\frac{3}{x}\)
⇒ log10 ( 10 × 0.555 ) = \(\frac{3}{x}\)
⇒ log10 ( 0.555 ) + 1 = \(\frac{3}{x}\) ..... (1)
Also, we have
(0.555)y = 1000
Taking log both the side
y log10 ( 0.555 ) = 3
⇒ log10 ( 5.55 ) = \(\frac{3}{x}\) ..... (2)
From equation (1) and (2), we get
\(\frac{3}{y}+1=\frac{3}{x}\)
⇒ \(\frac{1}{x}-\frac{1}{y}=\frac{1}{3}\)
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