CAT 2021 Question Paper (Slot 2) Question 54

Question 54

If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals


Correct Answer: 5

Solution

We have :
$$\log_2\left\{3+\log_3\left\{4+\log_4\left(x-1\right)\right\}\right\}=2$$
we get $$3+\log_3\left\{4+\log_4\left(x-1\right)\right\}=4$$
we get $$\log_3\left(4+\log_4\left(x-1\right)\ =\ 1\right)$$
we get $$4+\log_4\left(x-1\right)\ =\ 3$$
$$\log_4\left(x-1\right)\ =\ -1$$
x-1 = 4^-1 
x = $$\frac{1}{4}+1=\frac{5}{4}$$
4x = 5


View Video Solution


Create a FREE account and get:

  • All Quant CAT Formulas and shortcuts PDF
  • 30+ CAT previous papers with solutions PDF
  • Top 500 CAT Solved Questions for Free

Comments
cracku

Boost your Prep!

Download App