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If \(\log_5(\log_8(x^2 - 1)) = 0\), then a possible value of \(x\) is

Question and options

If log⁡5(log⁡8(x2−1))=0\log_5(\log_8(x^2 - 1)) = 0, then a possible value of xx is
  1. 22\sqrt{2}
  2. 2\sqrt{2}
  3. 2
  4. 3

Answer and explanation

Correct answer: D - 3

A log equal to 0 means its argument is 1, so log base 8 of (x squared - 1) = 1. Hence x squared - 1 = 8, x squared = 9 and x = 3 or -3; only 3 is offered. Trying 2 root 2 gives x squared - 1 = 7, which does not make the base-8 log equal to 1.

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