If (10011)x​=(631)10​ then what is the value of x?

To find the base x, expand (10011)x using powers of x: 1*x^4 + 0*x^3 + 0*x^2 + 1*x^1 + 1*x^0 = 631. This simplifies to x^4 + x - 630 = 0. Testing integer values, we find that when x equals 5, the equation holds true since 625 + 5 - 630 equals zero.