Logarithms Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
11). If \( \Large log_{2} x + log_{2} y \ge 6 \), then the least value of \( \Large \left(x + y\right) \) is
A). 4
B). 9
C). 16
D). 32
12). If \( \Large  4^{log_{3}\frac{31}{2}}  + 9^{log2^{2}} = 10^{log_{x}83} \), (x belongs to R), then x is:
A). 4
B). 9
C). 10
D). none of these
13). Which of the following is not true?
A). \( \Large \frac{1}{log_{3} \pi } + \frac{1}{log_{4} \pi }>2 \)
B). \( \Large log_{3}5 \)
C). \( \Large \sqrt{8x} = \frac{10}{3} => x = 16 \)
D). \( \Large log_{x} \left(a^{2}+1\right)<0 \), (a?0) then 0
14). If \( \Large y = \frac{1}{a^{1-log ax}} \) and \( \Large z = \frac{1}{a^{1+log_{a}y}} \) then x is equal to:
A). \( \Large \frac{1}{a^{1+log_{a}z}} \)
B). \( \Large \frac{1}{a^{z+log_{a}z}} \)
C). \( \Large \frac{1}{a^{1-log_{a}z}} \)
D). none of these
15). The least value of n in order that the sum of first n terms of an infinite series \( \Large 1 + \frac{3}{4} + \left(\frac{3}{4}\right)^{2} + \left(\frac{3}{4}\right)^{3}+ .... \) should differ from the sum of the series by less then \( \Large 10^{-6} \) is
[\( \Large\ Given\ log_{10}2=0.30103, log_{10}3=0.47712 \)]

A). 14
B). 27
C). 53
D). 57


16). Solution of the equation \( \Large x log^{x^{2}} = log3 \left(x+y\right) \) and \( \Large x^{2}+y^{2} = 65 \) is:
A). x = 8, y = 1
B). x = 1, y = 8
C). (x=8, y=1); (x=1, y=8)
D). none of the above
17). The identity \( \Large log_{a}n\ log_{b}n\ +\ log_{b}n\ log_{c}n\ +\ log_{c}n\ log_{a}n \) ls:
A). \( \Large \frac{log_{a}n\ log_{b}n\ log_{c}n}{log_{abc}n} \)
B). \( \Large \frac{log_{abc}n}{log_{a}n} \)
C). \( \Large \frac{log_{b}n}{log_{abc}n} \)
D). none of these
18). The least value of the expression \( \Large 2\ log_{10}x\ -\ logx\ \left(0.01\right) \) for x > 1, is:
A). 10
B). 2
C). -0.01
D). none of the above
19). \( \Large log_{10}1000 \) =
A). 3
B). 6
C). 8
D). 10
20). Simplify: \( \Large log_{10}2500 \)
A). 2
B). 1
C). 3
D). 4
Go to :
Total Pages : 4