To justify the definition of logarithms, is necessary to show that the equation {\displaystyle b^{x}=y\,} b^{x}=y\, has a solution x and that this solution is unique, provided that y is positive and b is positive and unequal to 1. A proof of that factor requires the intermediate value theorem from elementary calculus.[33] eorum states that a continuous function of that produces 2 values m and n also produces any value that lies between m and n. A function is continuous if it does not “jump”, that is, if its graph can be drawn without lifting the pen.