CAT Practice : Exponents and Logarithms

Carving a quadratic equations from an Exponents question is very useful.

Logartihm - Quadratic Equations

    Q.3: If 22x+4 – 17 × 2x+1 = –4, then which of the following is true?
    1. x is a positive value
    2. x is a negative value
    3. x can be either a positive value or a negative value
    4. None of these

 

  • Correct Answer
    Choice C. x can be either a positive value or a negative value

Explanatory Answer

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Detailed Solution

2x+4 – 17 × 2x+1 = – 4
2x+1 = y
22x+2 = y2
22(22x+2) – 17 × 2x+1 = –4
4y2 – 17y + 4 = 0
4y2 – 16y – y + y = 0
4y (y – 4) – 1 (y – 4) = 0
y = or 4
2x+1 = or 4
x + 1 = 2 or – 2
x = 1 or – 3
Answer choice (c)

Correct Answer: x can be either a positive value or a negative value



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More questions from Exponents and Logarithms

  1. Logarithm - Inequalities
  2. Logarithm - Simple
  3. Logartihm - Quadratic Equations
  4. Logartihm - Algebra
  5. Logarithm - Inequalities
  6. Logarithms - Different bases
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