CAT 2020 Question Paper | Quants Slot 1

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. In this question from the given equation, you have to find the value of the unknown variable Y. 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 5 : If log₄ 5 = (log₄ y) (log₆ √5), then y equals

Video Explanation

Explanatory Answer

log₄5 = log₄y × log₆√5
log₄5 ÷ log₄y = log_y5 = log₆√5 = k (Let’s assume this as k)
6^k = √5 ---> On squaring this {6^k}² = 5

log₄5 = log₄y × log₆√5
log_y5 = log₆√5
log_y5 = k
y^k = 5

{6^k}² = y^k = 5
{6²}^k = y^k
36^k = y^k
y = 36.

The question is "If log₄ 5 = (log₄ y) (log₆ √5), then y equals"

Hence, the answer is, " 36"