Question

If $x^y=y^x$ and x = 2y, then find the value of $x+y$. (Assume that $y\ne 0$)

• A. 3
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is B 6

We have,

$x^y=y^x$ …….. (1)

And $x=2y$ ……. (2)

On putting the value of $x$in equation $\left(2\right)$, we get

${\left(2y\right)}^y=y^{2y}$

$2^y.y^y=y^y.y^y$

$y^y=2^y$

$y\ln y=y\ln 2$

$\therefore y=2$

Therefore,

$x=4$

So,

$x+y=4+2$

$x+y=6$

Hence, this is the answer.