lim (a^x-b^x)/x =lim b^x{(a/b)^x-1}/x
f(x)=(a/b)^x とおくと　lim {(a/b)^x-1}/x =f'(0)=log(a/b)

lim b^x{(a/b)^x-1}/x = log(a/b)