# Recent questions tagged logarithms

1 vote
1
Let $x_1 > x_2>0$. Then which of the following is true? $\log \big(\frac{x_1+x_2}{2}\big) > \frac{\log x_1+ \log x_2}{2}$ $\log \big(\frac{x_1+x_2}{2}\big) < \frac{\log x_1+ \log x_2}{2}$ There exist $x_1$ and $x_2$ such that $x_1 > x_2 >0$ and $\log \big(\frac{x_1+x_2}{2}\big) = \frac{\log x_1+ \log x_2}{2}$ None of these
2
Which of the following is true? $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$ $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$ $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$ $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
3
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then $y=0$ $y=1$ $y=2$ $y=3$
4
The value of $\log _2 e – \log _4 e + \log _8 e – \log _{16} e + \log_{32} e – \cdots$ is $-1$ $0$ $1$ None of these
5
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is in Arithmetic progression (AP) Geometric progression (GP) Harmonic progression (HP) None of these
6
The value of $\log_{2}e-\log_{4}e+\log_{8}e-\log_{16}e+\log_{32}e-\cdots\:\:$ is $-1$ $0$ $1$ None of these
1 vote
7
The value of $\dfrac{1}{\log_2 n}+ \dfrac{1}{\log_3 n}+\dfrac{1}{\log_4 n}+ \dots + \dfrac{1}{\log_{2017} n}\:\:($ where $n=2017!)$ is $1$ $2$ $2017$ none of these
1 vote
8
The solution of $\log_5(\sqrt{x+5}+\sqrt{x})=1$ is $2$ $4$ $5$ none of these
9
If log 2= 0.030103, the number of digits in 2^64 is : a.18 b.19 c.20 d.21
10
What is the value of $\{ ( 1/ \log_3 60)+ (1/ \log_4 60 ) + (1/ \log_5 60) \}$? $0$ $1$ $5$ $60$
1 vote
11
The value of the expression $\dfrac{1}{1+ \log_u \: vw} + \dfrac{1}{1+ \log_v \: wu} + \dfrac{1}{1+\log_w uv}$ is _______ $-1$ $0$ $1$ $3$
1 vote
12
For integers, $a$, $b$ and $c$, what would be the minimum and maximum values respectively of $a+b+c$ if $\log \mid a \mid + \log \mid b \mid + \log \mid c \mid =0$? $\text{-3 and 3}$ $\text{-1 and 1}$ $\text{-1 and 3}$ $\text{1 and 3}$
13
For non-negative integers, $a, b, c$, what would be the value of $a+b+c$ if $\log a + \log b + \log c = 0$? 3 1 0 -1
14
Given that $\frac{\log P}{y-z} = \frac{\log Q}{z-x} = \frac{\log R}{x-y} = 10$ for $x \neq y \neq z$, what is the value of the product $PQR$? 0 1 $xyz$ $10^{xyz}$
1 vote
15
solve for x $3^{log^2_{3} x }$ + $x^{log_{3} x }$ = 162
16
Evaluate $\frac{1}{n^{\log_{2}n}}$
17
What is the difference among the following: $\log^²n , \log n^², \log\log n, (\log n)^²$
18
A value of $x$ that satisfies the equation $\log x + \log (x – 7) = \log (x + 11) + \log 2$ is $1$ $2$ $7$ $11$
19
$\log \tan 1^o + \log \tan 2^o + \dots + \log \tan 89^o$ is $\ldots$ $1$ $1/\sqrt{2}$ $0$ $−1$
If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is $343/125$ $25/343$ $-25/49$ $-49/25$
A table contains $287$ entries. When any one of the entries is requested, it is encoded into a binary string and transmitted. The number of bits required is. $8$ $9$ $10$ Cannot be determined from the given information. None of the above.
If $\log (\text{P}) = (1/2)\log (\text{Q}) = (1/3)\log (\text{R})$, then which of the following options is TRUE? $\text{P}^2 = \text{Q}^3\text{R}^2$ $\text{Q}^2=\text{P}\text{R}$ $\text{Q}^2 = \text{R}^3\text{P}$ $\text{R}=\text{P}^2\text{Q}^2$