Logarithms Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). If \( \Large log3 \times log4\ x > 0 \), then 
A). \( \Large x > 1 \)
B). \( \Large x > 4 \)
C). \( \Large x > 64 \)
D). none of these
2). \( \Large log \frac{1}{4} \left(a^{2}-1\right) < log_\frac{1}{2} \left(a+1\right)^{2}\)
A). \( \Large a<1 \)
B). \( \Large a<-1 \)
C). \( \Large a>1 \)
D). none of these
3). If \( \Large log_{e} \left(\frac{a+b}{2}\right) = \frac{1}{2} \left(log_{e} a+log_{e} b\right) \) then:
A). a = b
B). a = b/2
C). 2a = b
D). \( \Large a = \frac{b}{3} \)
4). If \( \Large 2 log \left(x+1\right)-10g \left(x^{2}-1\right) = log^{2} \), then x equals
A). 1
B). 0
C). 2
D). 3
5). The number \( \Large log 2^{7} \) is:
A). an integer
B). a rational number
C). an irrational number
D). a prime number


6). If \( \Large y = 2^{\frac{1}{logx}\left(8\right)} \), then x is equal to:
A). y
B). \( \Large y^{2} \)
C). \( \Large y^{3} \)
D). none of these
7). If \( \Large log_{05} \sin x = 1 - log_{05} \cos x \), then number of solution of \( \Large x ? \left[ -2 \pi , 2 \pi \right] \) is:
A). 1
B). 2
C). 3
D). 4
8). If a, b, c are in GP. then \( \Large log ax^{x}, log_{bx}x, log_{cx}x \) are in:
A). GP
B). HP
C). AP
D). none of these
9). Consider the following statements:
1. Solution of the inequality \( \Large log_{5} \left(x^{2}-11x+43\right)<2 \) is (0, 2)
2. If \( \Large [x - 1]^{ \left(log_{3}x^{2} - 2Logx^{9}\right)} =  \left(x - 1\right)^{7}  \), then x is 2 and 81.
Which of these is/are correct?

A). only(1)
B). only 2
C). both of these
D). none of these
10). \( \Large log \cos x \sin x \ge 2 \) and  \( \Large x \epsilon \left[ 0, 3 \pi \right] \), then \( \Large \sin x \) lines in the interval:
A). \( \Large \left[ 0, \frac{1}{2} \right] \)
B). \( \Large \left[\frac{\sqrt{5}-1}{2}, 1 \right] \)
C). \( \Large \left[ 0, \frac{\sqrt{5}-1}{2} \right] \)
D). none of these
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