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NDA 2016 Maths · Mathematics · Logarithms · medium

If log x 27=3/2, then x is equal to

Single correct option

If log⁡x27=32\log_x 27=\dfrac32, then xx is equal to
  1. A. 33
  2. B. 8181
  3. C. 99
  4. D. 27\sqrt{27}
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Answer: (C) 99

Converting to exponential form, x3/2=27=33x^{3/2}=27=3^3. Raising both sides to the power 23\tfrac23 gives x=32=9x=3^{2}=9. Checking: 93/2=279^{3/2}=27. The value 3 comes from dropping the fractional power.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake