# logic's question: lets assume I have variable x which it gives me volume 5a then what's the volume of 3x?

##### Junior Member
thank you very much for your explanation, very meaningful.
to sum up .. must I through my solution follow math's assumptions/rules? for example x=5a
how many 3x? I must according to math multiply x=5a by 3 so I get 3x=15a
so the answer for "how many 3x" =>15a , and that's because I used math arithmetic/rules..must I follow in every step math rules for getting correct logic?

#### HallsofIvy

##### Elite Member
IF you were given that "x= 5a" then, yes, multiplying on both sides by 3, "3x= 15a". But in your first post you didn't say "x= 5a". You said "I have variable x which it gives me volume 5a" which I would interpret as saying that you have some function that, applied to x, gives 5a. But there are infinitely many different functions, f, such that f(x)= 5a. One such is $$\displaystyle f(u)= \frac{5au}{x}$$. When u= x, $$\displaystyle f(x)= \frac{5ax}{x}= 5a$$. And for that function, $$\displaystyle f(3x)= \frac{5a(3x)}{x}= 15a$$. But another such function is $$\displaystyle f(u)= \frac{5ax}{u}$$. Again, $$\displaystyle f(x)= \frac{5ax}{x}= 5a$$. But now $$\displaystyle f(3x)= \frac{5ax}{3x}= \frac{5}{3}a$$.