CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

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}\\)

Video Explanation

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.