#### To determine

**To find:**

The value of *k* in the given expression.

#### Answer

k **= **e2.

#### Explanation

**Given:**

e2x=kx

**Formulae used:**

The substitution method to satisfy the equation

Consider e2x=kx

Hence, use the formulae of substitution method to satisfy the equation

Take log on both sides.

e2x=kx2x=lnk+12lnx

Determine k in form of *x*

⇒2lnk=4x−lnx⇒lnk=2x−lnx2⇒k=e2x−lnx2

Now there should be some value which satisfies the equation. Assume that it is 1.

At *x=*1.

k=e2

⇒e2x=e2x2x=2+12lnx4x=4+lnx

x=1 is the only solution which satisfy the equation 4x=4+lnx

Hence k=e2 is the solution.

**Conclusion: **Hence the value of *k *is e2.