CAT 2020 Question Paper | Quants Slot 3

CAT Previous Year Paper | CAT Quants Questions | Question 3

Logarithms is one of the most commonly tested topics in CAT exam. This topic plays a pivotal role in your CAT preparation. Questions from Logarithms have appeared consistently for several years in CAT exam. This question tests your understanding of the properties of Logarithms. If you're thorough with your fundamentals, then you're through. CAT Exam is known to test your fundamentals rather than high funda ideas. CAT Logarithms and Exponents is a favorite in CAT Exam, with every extra hour you log in for this topic, it becomes exponentially simpler.

Question 3 : Let loga30 = A, loga\\frac{5}{3}) = -B and log2a = \\frac{1}{3}), then log3a equals

  1. \\frac{2}{A+B-3})
  2. \\frac{A+B-3}{2})
  3. \\frac{A+B}{2}) - 3
  4. \\frac{2}{A+B}) - 3

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Explanatory Answer

Let loga30 = A be equation 1.
and loga\\frac{5}{3}) = -B be equation 2.

We are told that log2a = \\frac{1}{3})
log2a = \\frac{1}{3}) implies loga2 = 3

Dividing eqn(1) and eq(2) by loga2 = 3
We get; log230 = \\frac{A}{3}) and
log2\\frac{5}{3}) = -\\frac{B}{3})

log230 = log2(5 × 3 × 2)
\\frac{A}{3}) = log25 + log23 + log22
\\frac{A}{3}) = log25 + log23 + 1, let's call this equation 3

log2\\frac{5}{3}) = log25 - log23
-\\frac{B}{3}) = log25 - log23, let's call this equation 4

Solving equations 3 and 4 we get, log23 = \\frac{A+B-3}{6})
Dividing this by log2a = \\frac{1}{3}) we get,
log2a = \\frac{A+B-3}{2})

log2a = \\frac{A+B-3}{2}) implies loga2 = \\frac{2}{A+B-3})


The question is "Let loga30 = A, loga\\frac{5}{3}) = -B and log2a = \\frac{1}{3}), then log3a equals"

Hence, the answer is, "\\frac{2}{A+B-3})"

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