#### To determine

**To show:**

We have to show that the equation x1lnx=2 has no solution.

#### Answer

proved

#### Explanation

**Calculation:**

First, we write the equation

x1lnx=2

We know that

a=xy⇔x=a1/y

So,

x=21/1/lnx=2lnx

Since

logax=y⇔x=ay

So,

lnx=log2x=lnxln2

Or

ln2=1

Which is not possible. Thus, the equation has no solution.

Now, Consider the function fx=x1/lnx=y.

Or

x=ylnx

Or

lnx=logyx=lnxlny

lny=1

Or

y=e

**Conclusion:** proved