Base convertion and equations

Question

I am studying for an exam in my course, and I will certainly have a question of the kind:

In what base is the equation right, for example:

42-3=36

Another example:

(8*5+11)/4=12

I am wondering how to approach this kind of excercises, and how to solve them. I know how to convert from one base to another, but is there a method to solve these equations?

Thank you.

Answer 1

first equation: Here you can substract 2 on both sides:

$40-3=34$

Then add 3 on both sides:

$40=34+3_{10}$

3 is at any base 3. If you add only 2, on the right side becomes 36. So 6 is the biggest digit. Then it is clear what the base is.

For the second equation I find no base which makes the equation true.

greetings,

calculus