The number 1621 was subtracted from 6244 in base x. If the result was 4323,…

Explanation

 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