Question

The numbers in each of the following equalities are all expressed in the same base, r . Determine the radix r in each case for the following operations to be correct. (a) 14/2 = 5 (b) 54/4 = 1

Answer 1

a)r=6 b)r=0

Explanation:

Before to get started, Let's to express each number in base r.

We should take in account that it process is similar to express numbers in decimal base, except that in this case
`10^(n)` is replaced by
`r^(n)`.

a) 14=1x
`1*r^(1) +4*r^(0)  =r+4\\`

`2=2*r^(0) \\`

`5=5*r^(0)`

Replacing each number in base r on the equalitie a.

`(r+4)/(2) =5`

Solving this equation

`(r+4)=10\\r=6`

b)
`54=5*r^(1) +4*r^(0) =5r+4\\4=4*r^(0) \\1=1*r^(0)`

Replacing each number in base r on the equalitie b.

`(5r+4)/(4)=1`

Solving this equation:

`5r+4=4\\r=0`

Answer 2

a) r = 6

b) r = 0

Explanation:

See it in the pic.