# Answer the following: If log(x-y5)=12logx+12logy, show that x2 + y2 = 27xy - Mathematics and Statistics

Sum

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

#### 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