Question

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

Answer 1

211x=6A•16
211x=96A
211x=96A
___. ___
211. 211

x=96A
___
211


It's hard to show fractions on here :•)

Answer 2

$(6A)_{16}=6\cdot 16+10=106$
$(211)_x=2\cdot x^2+1\cdot x + 1=106$
$2 x^2+ x + 1-106=0$
$2\cdot x^2+ x -105=0$
$\Delta=1^2-4\cdot 2\cdot (-105)=1+840=841=29^2$
$x=\dfrac{-1+29}{2\cdot 2}=\dfrac{28}{4}=7$

The value of base x is equal to 7.