If 312 base 4+52 base n= 96 base 10 find n
It 124base n= 232 base 5 find n
312 base 4+52 base n= 96 base 10
( 3(4^2) + 1(4) + 2 ) + ( 5(n) + 2 ) = 96
54 + 5n + 2 = 96
5n = 40
n = 8
second equation:
124base n= 232 base 5
1(n^2) + 2n + 4 = 2(5^2) + 3(5) + 2
n^2 + 2n - 63 = 0
(n - 7)(n + 9) = 0
n = 7 or n = -9 , (don't know if your text allows negative bases, you decide)