For f(x) to be continuous, we must havef(0)​=x→0lim​f(x)=x→0lim​xlog(1+ax)−log(1−bx)​=x→0lim​axalog(1+ax)​+−bxblog(1−bx)​=α⋅1+b⋅1[ using x→0lim​xlog(1+x)​=1]​∴f(0)​=a+b=(a+b)​