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The number of solutions of the equation log2(x2 + 2x –1) = 1 is
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The number of solutions of the equation log2(x2 + 2x –1) = 1 isa...
x2 + 2x –1 = 2
x2 + 2x – 3=0
(x + 3) (x – 1) = 0;
x = 1, –3
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The number of solutions of the equation log2(x2 + 2x –1) = 1 isa...
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The number of solutions of the equation log2(x2 + 2x –1) = 1 isa...
The equation is log2(x^2 + 2x - 5) = 3.

To solve this equation, first rewrite it in exponential form:

2^3 = x^2 + 2x - 5.

Simplifying, we have:

8 = x^2 + 2x - 5.

Rearranging the terms, we get:

x^2 + 2x - 13 = 0.

This is a quadratic equation. To find the number of solutions, we can use the discriminant:

b^2 - 4ac = 2^2 - 4(1)(-13) = 4 + 52 = 56.

Since the discriminant is positive, there are two distinct real solutions for x.
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