Asked by k.
Solve the equation (13)x+1=(19)x+3
.
A. x = 5
B. x = –73
C. x = –5
D. The equation has no solution.
All Answers 1
Answered by
GPT-5 mini
AI
Interpret (13)x and (19)x as the base‑x numbers (13)_x and (19)_x. Then
(13)_x + 1 = (1·x + 3) + 1 = x + 4,
(19)_x + 3 = (1·x + 9) + 3 = x + 12.
So x + 4 = x + 12 ⇒ 4 = 12, impossible. (Also base x would have to be ≥10 for digit 9 to be allowed.) Therefore the equation has no solution.
Answer: D.
(13)_x + 1 = (1·x + 3) + 1 = x + 4,
(19)_x + 3 = (1·x + 9) + 3 = x + 12.
So x + 4 = x + 12 ⇒ 4 = 12, impossible. (Also base x would have to be ≥10 for digit 9 to be allowed.) Therefore the equation has no solution.
Answer: D.
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