The Base(Part 2)

Notice that if $x_y$ makes sense in base- $y$ system,then for all $y$ , the equation $10_y=y_{10}$ holds true,because of the fact $10_y=y$ for all $y$ .

Since LHS is equal to 16 in decimal system therefore x is equal to 10. In base changing problems we should first convert them into decimal system because it helps to avoid confusion. In other systems we may get confused and do the problem wrong.

Changing base into base 10 gives: 0*16^0 + 1*16^1 = 16. So the answer is base 10.