Determine the value of base x if (211) x = (6A) 16

convert 6A base 16 into base 10.

(6) (161) + (10) (160) = 96+10=106 (6) (161) + (10) (160) = 96+10=106

Then, let’s convert 211 base x into base 10, result must equal to 106.

(2) (x2) + (1) (x1) + (1) (x0) = 106 (2) (x2) + (1) (x1) + (1) (x0) = 106

2x2+x-105=02x2+x-105=0

Factoring the equation and exclude the non-integer result, we will get x=7x=7

it’s base 7.