CAT 2018 Logarithms Question (Hard)

Question

If log 2 5 log 3 a 3 and log 5 4a 12 log 2 b 3, then a b is equal to

Accepted Answer

Step 1 Given log base 2 of 5 log base 3 of a 3 5 log base 3 of a 2 8 log base 3 of a 3 a 3 27 Step 2 Second equation log base 5 of 4a 12 log base 2 of b 3 4a 12 log base 2 of b 5 125 Substitute a 27 4 27 12 log base 2 of b 125 108 12 log base 2 of b 125 log base 2 of b 5 b 2 32 Step 3 a b 27 32 59 F

CAT 2018

Quantitative

Logarithms

Hard

If log 2 (5 + log 3 a) = 3 and log 5 (4a + 12 + log 2 b) = 3, then a + b is equal to

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