Given that \( 6244_x - 1621_x = 4323_x \), find the value of \( x \). {Step 1: Convert to decimal:} \[6244_x = 6x^3 + 2x^2 + 4x + 4\] \[1621_x = 1x^3 + 6x^2 + 2x + 1\] \[4323_x = 4x^3 + 3x^2 + 2x + 3\] f{Step 2: Set up the equation:} \[(6x^3 + 2x^2 + 4x + 4) - (1x^3 + 6x^2 + 2x + 1) = 4x^3 + 3x^2 + 2x + 3\] {Step 3: Simplify the left side:} \[(6x^3 - 1x^3) + (2x^2 - 6x^2) + (4x - 2x) + (4 - 1) = 5x^3 - 4x^2 + 2x + 3\] {Step 4: Set the equation:} \[5x^3 - 4x^2 + 2x + 3 = 4x^3 + 3x^2 + 2x + 3\] {Step 5: Combine like terms:} \[5x^3 - 4x^3 - 4x^2 - 3x^2 + 2x - 2x + 3 - 3 = 0\] \[x^3 - 7x^2 = 0\] {Step 6: Factor the equation:} \[x^2(x - 7) = 0\] {Step 7: Solutions:} \[x = 7 \quad (\text{valid}), \quad x = 0 \quad (\text{not valid})\] \Thus, the base \( x \) is 7