To limit the exponent, you must limit the entire expression.

x * ln((x+c)/(x-c))

Taking the limit is not only a part of ln ((x+c)/(x-c)). In fact, although ln((x+c)/(x-c)) tends to zero, x tends to infinity, and it is impossible to determine that their product also tends to zero.

Robida's law can be used to limit x*ln((x+c)/(x-c)). The result is 2c. However, it is unnecessary to find the limit by this method, because the required limit can be found directly by the second method.