What base is a?

Question

72 a = 2 x (27 a)

what base is (a)?

Binary code is base 2, so what is a?

Answer 1

72 base a = 7a + 2
27 base a = 2a + 7

from the given condition

7a+ 2 = 2(2a +7) = 4a + 14

or a = 4

as there is a digit 7 base > 7.

so no solution

Answer 2

72 base a = 2 x (27 base a)
In base a the digits moving to the left represent 1, a, a², a³, ....

So 7a + 2 = 4a + 14
3a = 12
a = 4

72 base 4 = 30 = actually 132 base 4
27 base 4 = 15 = actually 33 base 4
(there is no 7 base 4 ... the only allowable digits in base 4 are 0, 1, 2, 3)

Answer 3

Go with the definition of the base:
72(base)a = 7a + 2
27(base)a = 2a + 7

7a +2 = 2 x (2a + 7)

7a + 2 = 4a +14

3a = 12

a = 4

a cannot be 4, since there are no 7's in base 4. Something is amiss with your notation (Y!A is tough on mathematical notation) or the problem itself.

Answer 4

I do not iunderstan the question. that is why are you talking about base ???

72 a = 2(27a)
from thia it follows immdetialty that a = 0.