If log₁₀ 2 = 0.3010 and log₁₀ 3 = 0.4771, evaluate log₁₀ 4.5

JAMB Mathematics 2023 49 views

If log₁₀ 2 = 0.3010 and log₁₀ 3 = 0.4771, evaluate log₁₀ 4.5

  1. 0.6532 ✓
  2. 0.3010
  3. 0.7781
  4. 0.1761

Explanation

Step 1: Express 4.5 in terms of 2 and 3
4.5 = 9/2 = 3²/2

Step 2: Apply logarithm
log₁₀(4.5) = log₁₀(3²/2)

Step 3: Use quotient rule
log₁₀(3²/2) = log₁₀(3²) – log₁₀(2)

Step 4: Apply power rule
log₁₀(3²) = 2 × log₁₀(3)
= 2 × 0.4771
= 0.9542

Step 5: Calculate final answer
log₁₀(4.5) = 0.9542 – 0.3010
= 0.6532

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