CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

The question is from Log and Exponents. We can solve this easily using log identities. We need to find out the value of a log given an equation. 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 8: log_xy + log_yx² = 3. Find log_xy³.

1. 4
2. 3
3. 3^1/2
4. 3^1/16

Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: Application of Basic Identities!!

log_xy + log_yx² = 3
Let a = log_xy
log_x3 = \\frac{1}{log_3{x}}\\)
log_yx² = 2log_yx
We know that log_yx = \\frac{1}{log_x{y}}\\)
Hence form above log_yx = \\frac{1}{a}\\)
Now rewritting the equation log_xy + log_yx² = 3
Using a we get a + \\frac{2}{a}\\) = 3
i.e., a² - 3a + 2 = 0
Solving we get a = 2 or 1
If a = 2, Then log_xy = 2 and log_yx³ = 3
log_xy = 3 * 2 = 6
Or
If a = 1, Then log_xy = 1 and log_yx³ = 3
log_xy = 3 * 1 = 3

The question is "Find log_xy³."

Hence, the answer is "3".

Choice B is the correct answer.