CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

The question is from Log and Exponents. This questions is about Logarithm - Different bases. We need to find out the value of log in terms of a and b based on given another two log values. 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 6: log₅x = a (This should be read as log X to the base 5 equals a) log₂₀x = b. What is log_x10?

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

Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: When we change the base, Log questions become far tougher.

Given, log₅x = a
log₂₀x = b
log_x5 = \\frac{1}{a}\\)
log_x20 = \\frac{1}{b}\\)
log_x\\frac{100}{5}\\) = \\frac{1}{b}\\)
log_x100 - log_n5 = \\frac{1}{b}\\)
=> 2log_x10 - \\frac{1}{a}\\) = \\frac{1}{b}\\)
log_x10 = \\frac{1}{2}\\)(\\frac{1}{a}\\) + \\frac{1}{b}\\))
log_x10 = \\frac{a + b}{2ab}\\)

The question is "What is log_x10?"

Hence, the answer is "\\frac{a + b}{2ab}\\)".

Choice A is the correct answer.