Recent questions tagged logarithms

6 votes
5 answers
1
For positive non-zero real variables $x$ and $y$, if\[\ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)]\]then, the value of $\frac{x}{y}+\frac{y}{x}$ is$1$$1 / ...
1 votes
1 answer
2
If $x$ satisfies the equation $4^{8^{x}}=256$, then $x$ is equal to __________.$\frac{1}{2}$ $\log _{16} 8$$\frac{2}{3}$$\log _{4} 8$
2 votes
0 answers
5
$\log _{2} x \times \log _{x/64}2 = \log _{x/16}2$x=?Please provide elaborative answer.
2 votes
1 answer
6
Which of the following is true ? $\log_{17} 275 = \log_{19} 375$$\log_{17} 275 \log_{19} 375$$\log_{17} 275 < \log_{19} 375$None of these
2 votes
1 answer
9
Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then$y=0$$y=1$$y=2$$y=3$
1 votes
2 answers
10
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
4 votes
1 answer
11
The sequence $\dfrac{1}{\log_{3} 2},\dfrac{1}{\log_{6} 2},\dfrac{1}{\log_{12} 2},\dfrac{1}{\log_{24} 2}\cdots$ is inArithmetic progression (AP)Geometric progression (GP)H...
1 votes
1 answer
12
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
3 votes
2 answers
13
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
2 votes
2 answers
14
The solution of $\log_5(\sqrt{x+5}+\sqrt{x})=1$ is$2$$4$$5$none of these
2 votes
0 answers
15
If log 2= 0.30103, the number of digits in 2^64 is :a.18 b.19 c.20 d.21
5 votes
1 answer
17
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$