Maharashtra State BoardHSC Science (General) 11th
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Answer the following: If log(x-y5)=12logx+12logy, show that x2 + y2 = 27xy - Mathematics and Statistics

Sum

Answer the following:

If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy

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Solution

`log ((x - y)/5) = 1/2 logx + 1/2 log y`

Multiplying throughout by 2, we get

`2log ((x - y)/5)` = log x + log y

∴ `log((x - y)/5)^2` = log xy

∴ `(x - y)^2/25` = xy

∴ x2 – 2xy + y2 = 25xy

∴ x2 + y2 = 27xy

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 6 Functions
Miscellaneous Exercise 6 | Q II. (28) | Page 131
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