How do you explain the concept of logarithm to a five year old? Okay, I understand that it cannot be explained to a 5 year old. But how do you explain the logarithm to primary school students?


I recently proceeded as above with more than 5 year old students ( in fact 17-18 y. old). Simply I was surprised to see that they seemed to get it immediatly; which made me suppose that much younger students could grasp this explanation. 
I think that students already have a " logarithm  box" in their head. I mean, before having heard the term logarithm, they already have the concept of " the power to which I have to raise number $5$ to get number $25$", or "the power to which I have to raise number $2$ to get number $8$". 
If this  assumption  is correct, teaching what is a logarithm simply amounts to giving a name to this concept, to this " logarithm box". 
