JEE Maths - Logarithm

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Question - 1

Consider an equation[log20l]+[log202]+.....[log20 x]= x here[x]is greatest integer function. Find the value of x.

  • A 418
  • B 417
  • C 419
  • D 209

Question - 2

lf p= log12 18, q =log24 54 then the value of pq + 5(p-q) is

  • A 0
  • B 4
  • C 1
  • D 9

Question - 3

Positive numbers x, y and z satisfying xyz = 10009 and (log10x) (log10y) + (log10x) log10z) + (log10y) (log10 z) = 6. Find the value of (log10x)2+ (log10y)2 + (log10z)2

  • A 4
  • B 6
  • C 5
  • D None of these

Question - 4

Find xyz if log2 x + log4 y + logo4 z = 2, log9 x + log3 y + logo9 z = 2, log16 x + log16 y + logo4 z = 2

  • A 24
  • B 32
  • C 12
  • D None of these

Question - 5

For \(x, v \in N, \text { if } 3^{2 x-y+1}=3^{y-2 x+1}-8\) and \(\log _{6}\left|2 x^{2} y-x y^{2}\right|=1+\log _{36}(x y)\) then point (x,y) lies in which quadrant?

  • A lies on axis
  • B lst quadrant
  • C 4th quadrant
  • D None of these

Question - 6

Which of the following is/are true?

  • A \(\log _{2}^{3}<\log _{5}^{17}\)
  • B \(\log _{2}^{24}\left(\log _{96}^{2}\right)^{-1}-\log _{2}^{192}\left(\log _{12}^{2}\right)^{-1}=3\)
  • C \(\left(\log _{2}^{5}\right)^{2}>\log _{2}^{20}\)
  • D \(\log _{10}^{5} \cdot \log _{10}^{20}+\left(\log _{10}^{2}\right)^{2}=1\)

Question - 7

If \(\frac{\log _{2} x}{4}=\frac{\log _{2} y}{6}=\frac{\log _{2} z}{3 k} \text { and } \mathrm{x}^{3} \mathrm{y}^{2} \mathrm{z}=1\) then k is equal to ___________
463k

  • A -8
  • B -4
  • C 0
  • D \(\log _{2}\left(\frac{1}{256}\right)\)

Question - 8

There exist positive integers A, B and C with no common factors greater than l, such that \(\mathrm{A} \log _{200} 5+\mathrm{B} \log _{200} 2=\mathrm{C}\) The sum A+ B + C equals ______.

  • A A = 2
  • B B = 3
  • C C = 1
  • D A + B = 5

Question - 9

If \(\log _{1(0)}|x+y|=\frac{1}{2} \text { and } \log _{10} y-\log _{10}|x|=\log _{100} 4\) then _________

  • A |x| < 12
  • B y > 12
  • C x < 5
  • D |y| < 20

Question - 10

Which of the following is true about the roots of \(\log _{2 x+3}\left(6 x^{2}+23 x+21\right)=4-\log _{3 x+7}\left(4 x^{2}+12 x+9\right)\)
 

  • A Equation has only one solution 
  • B Sum of the roots is negative
  • C roots must be less than 2
  • D At least one root is positive
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