CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions | Logarithms and Exponents | Logarithm - Algebra

The question is from Log and Exponents. A question that combines logarithm with Algebra. We need to find out a logarithm in terms of a and b. With every extra hour you log in for this topic, it becomes exponentially simpler. CAT Logarithms and Exponents is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 4: If log1227 = a, log916 = b, find log8108.

  1. \\frac{2(a + 3)}{3b}\\)
  2. \\frac{2(a + 3)}{3a}\\)
  3. \\frac{2(b + 3)}{3a}\\)
  4. \\frac{2(b + 3)}{3b}\\)

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Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: 2 can be expressed as a power of 3, 3 can be expressed as a power of 5. Do not live in the world that has only rational numbers; it is irrational to do that.

log8108 = log8(4 * 27)
log8108 = log84 + log827
=> log84 = \\frac{2}{3}\\)
log827 = \\frac{log_16{27}}{log_16{8}}\\)
log827 = \\frac{log_16{27}}{3/4}\\)
log827 = \\frac{4}{3}\\) log1627
log827 = \\frac{4}{3}\\) \\frac{log_9{27}}{log_9{16}}\\)
log827 = \\frac{4}{3}\\) \\frac{\\frac{3}{2}}{log_9{16}}\\)
log827 = 2 * log169
log916 = b
log169 = \\frac{1}{b}\\)
log827 = \\frac{2}{b}\\)
log8108 = \\frac{2}{3}\\) + \\frac{2}{b}\\)
= 2(\\frac{1}{3}\\) + \\frac{1}{b}\\))
= \\frac{2(b + 3)}{3b}\\).

The question is "find log8108."

Hence, the answer is "\\frac{2(b + 3)}{3b}\\)".

Choice D is the correct answer.


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