>> Elementary Mathematics >> Logarithms
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