Answer:
a)r=6 b)r=0
Step-by-step 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 [tex]10^{n}[/tex] is replaced by [tex]r^{n}[/tex].
a) 14=1x[tex]1*r^{1} +4*r^{0} =r+4\\[/tex]
[tex]2=2*r^{0} \\[/tex]
[tex]5=5*r^{0}[/tex]
Replacing each number in base r on the equalitie a.
[tex]\frac{r+4}{2} =5[/tex]
Solving this equation
[tex](r+4)=10\\r=6[/tex]
b) [tex]54=5*r^{1} +4*r^{0} =5r+4\\4=4*r^{0} \\1=1*r^{0}[/tex]
Replacing each number in base r on the equalitie b.
[tex]\frac{5r+4}{4}=1[/tex]
Solving this equation:
[tex]5r+4=4\\r=0[/tex]
