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Are you one of the CAT aspirants who is not content with their CAT preparation online? Do you lack confidence when somebody asks you about your CAT preparation? One important thing that could be missing in your schedule could be CAT previous year paper. These are a vital component and need to be covered by all the people preparing for the CAT exam. Solving questions from CAT previous year paper will give you a glimpse of what to expect in the CAT Question Paper and in turn be ready for any elements of surprises that you find in your exam. Dont wait for you to finish the CAT Syllabus for proceeding with these, solve one question from Logarithms taken from CAT 2019 Question Paper right now without looking at the solutions. See if you can solve it correctly!

Question 1 : The real root of the equation 26x + 23x+2 - 21 = 0 is

  1. \\frac{log_{2}3}{3})
  2. log29
  3. \\frac{log_{2}7}{3})
  4. log227

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Explanatory Answer

Given equation - 26x + 23x+2 - 21 = 0
The idea is to convert the above equation to a quadratic one.
So, 26x =
Let y =
Now, 26x + 23x+2 - 21 = 0 can be rewritten as + 22.23x - 21 = 0
y2 + 4y - 21 = 0
Solving the above quadratic equation,
(y + 7) (y - 3) = 0
So, y = -7 or +3
y = => y should always be positive
Therefore, y = -7 is not a valid solution. So, only y = +3 exists.
= 3
Taking log on both sides,
3x =
x = , which is the real solution to the given equation

The question is "The real root of the equation 26x + 23x+2 - 21 = 0 is"

Hence, the answer is \\frac{log_{2}3}{3})

Choice A is the correct answer.


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