Home | About Indiatry | Login | Register

    • ( 1 ) Evaluate: log9 27 - log27 9

    • 1) 2-Mar
    • 2) 6-May
    • 3) 1
    • 4) 3-Feb
    • Discussion in forum
      Answer : 2) 6-May
      Solution : log9 27 - log27 9
      => (log 27/log 9) - (log 9/log 27)
      => (log 33/log 32) - (log 32/log 33)
      => (3log 3/2log 3) - (2log 3/3log 3)
      => (3/2) - (2/3) = 5/6








      discussion


      Answer : 2) 6-May

    • ( 2 ) If log64 7 = x log4 7 then x = __________

    • 1) 4
    • 2) log464
    • 3) 3-Jan
    • 4) log43
    • Discussion in forum
      Answer : 3) 3-Jan
      Solution : log64 7 = x log4 7
      => (log 7/log 64) = x (log 7/log 4)
      => (log 7/log 43) = x (log 7/log 4)
      => (log 7/3log 4)* (log 4/log 7) = x
      => x = 1/3








      discussion


      Answer : 3) 3-Jan

    • ( 3 ) if ax = by, then

    • 1) log a/log b = x/y
    • 2) log a/b = x/y
    • 3) log a/log b = y/x
    • 4) None of these
    • Discussion in forum
      Answer : 3) log a/log b = y/x
      Solution : ax = by
      taking log both side
      log ax = log by
      => xlog a = ylog b
      => log a/log b = y/x








      discussion


      Answer : 3) log a/log b = y/x

    • ( 4 ) If logx (xy) = x, then logy (xy) is :

    • 1) 1/a
    • 2) a/(a+1)
    • 3) a/(1-a)
    • 4) a/(a-1)
    • Discussion in forum
      Answer : 4) a/(a-1)
      Solution : Given,
      logx (xy) = a
      => log xy/log x = a
      => (log x + log y)/log x = a
      => (log x/log x) + (log y/log x) = a
      => 1 + (log y/log x) = a
      => (log y/log x) = a - 1.................(1)
      logy (xy)
      => log xy/log y
      => (log x + log y)/log y
      => (log x/log y) + (log y/log y)
      => (1/a -1) + 1 (from equation (1)]
      => (1 + a - 1)/(a - 1)
      => a/(a - 1)








      discussion


      Answer : 4) a/(a-1)

    • ( 5 ) if log 2 = 0.30103, then the value of log2 10 is:

    • 1) 699/301
    • 2) 1000/301
    • 3) 0.301
    • 4) 0.699
    • Discussion in forum
      Answer : 2) 1000/301
      Solution : log2 10 = 1/log10 2 = 1/0.3010 = 10000/3010 = 1000/301.








      discussion


      Answer : 2) 1000/301

    • ( 6 ) If log10 125 + log10 8 = x, then x is equal to:

    • 1) 3
    • 2) -3
    • 3) 3-Jan
    • 4) 0.064
    • Discussion in forum
      Answer : 1) 3
      Solution : log10 125 + log10 8 = x
      => log10 (125*8) = x
      => log10 1000 = x
      => log10 103 = x
      => 3log1010 = x
      => x = 3.








      discussion


      Answer : 1) 3

    • ( 7 ) Evaluate: log100 (0.01)

    • 1) 1
    • 2) 0
    • 3) -1
    • 4) -2
    • Discussion in forum
      Answer : 3) -1
      Solution : Let log100 (0.01) = n
      Then, (100)n = 0.01 = 1/100 = (100)-1
      so, n = -1
      log100 (0.01) = -1








      discussion


      Answer : 3) -1

    • ( 8 ) The value of log5 (1/125) is :

    • 1) 3
    • 2) -2
    • 3) -3
    • 4) 2
    • Discussion in forum
      Answer : 3) -3
      Solution : Let log5 (1/125) = x
      Then, 5x = (1/125) = (1/53) = 5-3
      x = - 3








      discussion


      Answer : 3) -3

    • ( 9 ) logx(9/32) = -1/8, find the value of x

    • 1) (9/32)8
    • 2) (9/32)2
    • 3) (32/9)8
    • 4) (32/9)2
    • Discussion in forum
      Answer : 3) (32/9)8
      Solution : logx(9/32) = ?1/8
      => x-1/8 = 9/32
      => 1/x1/8 = 9/32
      => x1/8 = 32/9
      => x = (32/9)8








      discussion


      Answer : 3) (32/9)8

    • ( 10 ) If log(a/b) + log(b/a) = log(a+b), then

    • 1) a = b
    • 2) a + b = 1
    • 3) a - b = 1
    • 4) a2 - b2 = 1
    • Discussion in forum
      Answer : 2) a + b = 1
      Solution : log(a/b) + log(b/a) = log(a + b)
      => log [(a/b) * (b/a)] = log(a + b)
      => log(1)=log(a + b)
      => a + b = 1








      discussion


      Answer : 2) a + b = 1





Top