Discussion

Explanation:

Given, (543)₆ = (317)_k,

∴ 5 × 6² + 4 × 6 + 3 × 1 = 3 × k² + 1 × k + 7 × 1
 
⇒ 207 = 3k² + k + 7

⇒ 3k² + k – 200 = 0

Solving this quadratic equation, we get,

k = -25/3 or 8

Since base cannot be -ve.

∴ k = 8.

Hence, 8.

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