manpreetsingh86 wrote:

If x and y are positive numbers such that \(x^y = y^x\) and \(y=9x\), then the value of x is

a) \(9\)

b)\(\frac{1}{9}\)

c) \(\sqrt[9]{9}\)

d) \(\sqrt[3]{9}\)

e) \(\sqrt[4]{3}\)

\(x^y = y^x\) and \(y=9x\)

-> \(x^{9x}= (9x)^x\)

-> \(x^x (x^{8x} - 9^x) = 0\)

-> \(x^{8x} = 9^x = 3^{2x} =(\sqrt[2]{3})^{4x} = (\sqrt[4]{3})^{8x}\)

-> \(x = \sqrt[4]{3}\)

_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95

UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".