Test: Logarithm- 1 - UPSC MCQ

• Since log_a a = 1, so log₁₀ 10 = 1.
• log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3 
  ∴ log (2 + 3) ≠ log (2 x 3)
• Since loga 1 = 0. so logio 1 = 0.
• log (1 + 2 + 3) = log 6 
   log (1 x 2 x 3) = log 1 + log 2 + log 3=log (6). 

So. option (b) is incorrect.

Given, log 27 = 1.431
⇒ log (3³) = 1.431
⇒ 3 log 3 = 1.431
⇒ log 3 = 0.477
∴ log 9 = log (3²) = 2 log 3
⇒ (2 x 0.477) = 0.954

⇒ - log₁₀ (7 x 10)
⇒ - (log₁₀ 7 + log₁₀ 10)
⇒ - (a + 1)

log₁₀ 80 = log₁₀ (8 x 10)
⇒ log₁₀ 8 + log₁₀ 10
⇒ log₁₀(2³) + 1
⇒ 3 log₁₀ 2 + 1
⇒ (3 x 0.3010) + 1
⇒ 1.9030

log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1

⇒ log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + log₁₀ 10

⇒ log₁₀ [5 (5x + 1)] = log₁₀ [10(x + 5)]

⇒ 5(5x + 1) = 10(x + 5)

⇒ 5x + 1 = 2x + 10

⇒ 3x = 9

⇒ x = 3.

Given expression = 1/log₆₀ 3 + 1/log₆₀ 4 + 1/log₆₀ 5
= log₆₀ (3 x 4 x 5)
= log₆₀ 60
= 1.