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If $\log_{2}[ \log_{7} (x^{2}-x+37)]=1$ then what could be the value of $x$?

  1. $3$
  2. $5$
  3. $4$
  4. None of these
  5. $c$
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what is the option E?
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We know that loga x = y, then x = ay    

Therefore, on comparing with the given equation we get  log7 ( x^2 - x + 37 ) = 2^1 = 2 and furthermore from this we can say that x^2 - x + 37 = 7^2 = 49

x^2 - x +37 - 49 = 0

x^2 - x - 12 = 0

on solving the given equation we get x = 4 or x = -3

The value that satisfies the given answer-choices is x = 4.

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