Question

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Answer 1

Question:

• If ${x}^{y}={y}^{x}$ and x = 2y, then :
• (a) y = 1
• (b) x = 4
• (c) x = 2
• (d) y = 0

Answer:

$\large\bold\red{(b)x=4}$

Step-by-step explanation:

Given,

${x}^{y} = {y}^{x}$

And,

$x = 2y$

Substituting the values,

We get,

$= > {(2y)}^{y} = {y}^{2y} \\ \\ = > {2}^{y} \times {y}^{y} = {y}^{y + y} \\ \\ = > {2}^{y} \times {y}^{y} = {y}^{y} \times {y}^{y} \\ \\ = > {2}^{y} = {y}^{y} \\ \\ = > \bold{ y = 2}$

Therefore,

We get,

$= > x = 2 \times 2 \\ \\ = > \bold{ x = 4}$

Hence,

(b) x = 4 is correct answer.

Answer 2

Answer:

$\huge\bf\purple{(c)\: x =4}$

$\huge\bf\red{Given:-}$

• x^y=y^x

• x=2y

$\huge\bf\green{Solution..}$

• x^y=y^x.........(i)

• x=2y........................(ii)

By substituting the value of x into the (i) equation we get,

or, ( 2y)^y=y^2y

or, 2^y× y^y=y^(y+y)

or, 2^y × y ^y=y^y × y^y

or, 2^y=y^y

So, y =2

Then, x =2y

or, x =2 × 2

So, x =4

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