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Reviewed CSCA Mathematics question · Standard

If log_2 (x) + log_2 (x + 2) = 3, what is the value of x?

  1. 2
  2. 4
  3. -4
  4. 1
Show the answer and explanation

Correct answer

A. 2

Principle or equation

Use the logarithm product rule: log_b A + log_b B = log_b (AB). Then convert the logarithmic equation to exponential form.

Why this answer is correct

log_2 [x(x+2)] = 3 ⇒ x(x+2) = 2^3 = 8 ⇒ x^2 + 2x - 8 = 0 ⇒ (x+4)(x-2)=0 ⇒ x = -4 or x = 2. Since the logarithm requires x > 0 and x+2 > 0, x = -4 is extraneous. Thus x = 2.

Example

Check: log_2 2 + log_2 4 = 1 + 2 = 3.

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