Find the value of y if 402y = 102ten

JAMB Mathematics 2023 55 views

Find the value of y if 402ᵧ = 102₁₀

  1. 2
  2. 3
  3. 4
  4. 5 ✓

Explanation

Step 1: Expand base y number in decimal
402ᵧ = 4 × y² + 0 × y¹ + 2 × y⁰
= 4y² + 0 + 2
= 4y² + 2

Step 2: Set equal to decimal value
4y² + 2 = 102

Step 3: Solve for y²
4y² = 102 – 2
4y² = 100
y² = 25

Step 4: Find y
y = ±√25
y = ±5

Step 5: Choose valid base
A base must be positive and greater than the largest digit (4)
Therefore y = 5

Verify: 4(5²) + 2 = 4(25) + 2 = 100 + 2 = 102 ✓

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