Find base n if 126n=86

Answer 1

To find the base, we need to solve for n. We can start by isolating n by dividing both sides of the equation by 126:

```
126n = 86
n = 86/126
```

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

```
n = (43/63)
```

We can see that the base must be a number that makes the fraction $\frac{43}{63}$ equal to a whole number. We can check different bases by expressing 43 and 63 in terms of that base:

```
43 = 4b + 3
63 = 6b + 3
```

We can see that any base that satisfies these equations would work. One possible solution is base 10, which gives:

```
43 = 4(10) + 3
63 = 6(10) + 3
```

So the answer is base 10.