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.