If A = log27625 + 7log1113 and B = log9125 + 13log107

If A = log₂₇625 + 7log₁₁13 and B = log₉125 + 13log₁₀7 then which of the following is true ?

1. A > B
2. A < B
3. A =B
4. can't say

Correct Option: B

A = log₂₇625 + 7log₁₁¹³
= log_3³5⁴ + 7 log₁₁13
= 4/3 log₃ 5 + 7 log₁₁13
B = log₉125 + 13 log₁₁7 = log₃² 5³ + 13 log₁₁⁷
= 3/2 log₃ 5 +13 log₁₁ 7
Let log₃ 5 = x and by the above rule
7 log₁₁ 13 = 13 log₁₁ 7
Therefore, A = 4/3 x + 13 log₁₁ 7
and B = 3/2 x + 13 log₁₁ 17
clearly, A < B hence (B) is the correct answer.

Logarithm

Aptitude

Correct Option: B