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.