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If \(\log_4 x = a\) and \(\log_{25} x = b\), then \(\log_x 10\) is

Question and options

If log⁡4x=a\log_4 x = a and log⁡25x=b\log_{25} x = b, then log⁡x10\log_x 10 is
  1. a+b2\dfrac{a + b}{2}
  2. a−b2ab\dfrac{a - b}{2ab}
  3. a+b2ab\dfrac{a + b}{2ab}
  4. a+b2(a−b)\dfrac{a + b}{2(a - b)}

Answer and explanation

Correct answer: C - \(\dfrac{a + b}{2ab}\)
log_x 4=1/a gives log_x 2=1/(2a); log_x 25=1/b gives log_x 5=1/(2b). log_x 10=1/(2a)+1/(2b)=(a+b)/(2ab).

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