Question

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

Answer 1

`211_x=2x^2+x+1`

`6A_(16)=106_(10)`


`\implies 2x^2+x+1=106\iff 2x^2+x-105=(x-7)(2x+15)=0`

This has two solutions,
`x=7` and
`x=-\frac{15}2`.