Show that … is twice as large as

This problem is about the derivative $dy/dx=c{b}^x$.

Show that $C={\lim }_{h\to 0}(100^h-1)/h$ is twice as large as $c={\lim }_{h\to 0}(10^h-1)/h$. (Replace the last $h$'s by $2h$.)

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.1 An Overview, #28