Limits Continuity And Differentiability

The value of \(k(k > 0)\), for which the function \(f(x)=\frac{\left(e^x-1\right)^4}{\sin \left(\frac{x^2}{k^2}\right) \log \left(1+\frac{x^2}{2}\right)}\), where \(x \neq 0\) and \(f(0)=8\)