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  • Question
  • If log 1227 =a then log 616 is?


  • Options
  • A. 4(3 - a) / 3 + a
  • B. 4(3 + a) / 3 - a
  • C. 3 + a / 4(3 - a)
  • D. 3 - a / 4(3 + a)

  • Correct Answer
  • 4(3 - a) / 3 + a 

    Explanation

    ? log1227 = a
    ? log 27 / log 12 = a
    ? a log 12 = log 33
    ? a log ( 3 x 4 ) = 3 log 3
    ? a[log 3 + log 4] = 3 log 3
    ? a log 4 + a log 3 = 3 log 3
    ? a log 22 = ( 3 - a) log 3
    ? 2a log 2 = (3 - a) log 3
    ? log 2 / log 3 = (3 - a) / 2a
    Now log616 = log16 / log 6 = log 24 / log (2 x 3) = 4 log 2 / ( log 2 + log 3)
    = [4 (log 2 / log 3)] / [(log 2 / log 3) + 1]
    = 4[(3 - a) / 2a] / [{(3 - a) / 2a } + 1]
    = 4(3 - a) / (3 + a)


  • More questions

    • 1. 
      ?. x 4 ? 227 = 398
      ?. y 2 + 321 = 346

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 2. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

    • Options
    • A. Sunday
    • B. Saturday
    • C. Tuesday
    • D. Wednesday
    • Discuss
    • 3. 1, 4, 9, 16, 23, 25, 36

    • Options
    • A. 9
    • B. 23
    • C. 25
    • D. 36
    • Discuss
    • 4. 
      A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got ? 2100 less than P, then how much amount did Q receive?

    • Options
    • A. ? 2500
    • B. ? 2000
    • C. ? 1500
    • D. Couldn't be determined
    • Discuss
    • 5. 
      If a : b = b : c, then ratio a 4 : b 4 is equal to

    • Options
    • A. ac : b2
    • B. a2 : c2
    • C. c2 : a2
    • D. b2 : ac
    • Discuss
    • 6. 
      A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.

    • Options
    • A. 3 km/h
    • B. 4 km/h
    • C. 4.5 km/h
    • D. 9 km/h
    • Discuss
    • 7. 
      A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?

    • Options
    • A. 2 h
    • B. 21/2 h
    • C. 51/2 h
    • D. 4 h
    • Discuss
    • 8. 
      Find the least number by which 175760 be devided to make it a perfect cube.

    • Options
    • A. 10
    • B. 20
    • C. 100
    • D. 5
    • Discuss
    • 9. 
      The roots of the equation x2 + px + q = 0 are equal if :

    • Options
    • A. p2 = 2q
    • B. p2 = 4q
    • C. p2 = - 4q
    • D. p2 = - 2q
    • Discuss
    • 10. 
      Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?

    • Options
    • A. 1 : 3
    • B. 1 : 8
    • C. 1 : 9
    • D. 1 : 18
    • Discuss


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