# Recent questions tagged logarithms

1 vote
1
For a real number $a,$ if $\dfrac{\log_{15}a + \log_{32}a}{(\log_{15}a)(\log_{32}a)} = 4$ then $a$ must lie in the range $a>5$ $3<a<4$ $4<a<5$ $2<a<3$
1 vote
2
If $\log_{2} [3+ \log_{3} \{ 4+ \log_{4} (x-1) \}] – 2 = 0$ then $4x$ equals
1 vote
3
If $5 – \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}},$ then $100x$ equals
4
If $\log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B}$ and $\log_{2} a = 1/3,$ then $\log_{3}a$ equals $\frac{2}{\text{A + B}} \;– 3$ $\frac{\text{A + B} - 3}{2}$ $\frac{2}{\text{A + B} – 3}$ $\frac{\text{A + B}}{2}\; – 3$
5
$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals
6
The value of $\log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right),$ for $1 < a \leq b$ cannot be equal to $– 0.5$ $1$ $0$ $– 1$
7
If $\log_4 5=\left ( \log _{4}y \right )\left ( \log _{6}\sqrt{5} \right )$, then $y$ equals
1 vote
8
If $y$ is a negative number such that $2^{y^{2}\log _{2}3}=5^{\log_{2}3}$, then $y$ equals $\log _{2}\left ( \frac{1}{3} \right )$ $-\log _{2}\left ( \frac{1}{3} \right )$ $\log _{2}\left ( \frac{1}{5} \right )$ $-\log _{2}\left ( \frac{1}{5} \right )$
9
If $\log _{e}x+\log _{e}(1+x)=0,$ then: $x^{2}+x-1=0$ $x^{2}+x+1=0$ $x^{2}+x-e=0$ $x^{2}+x+e=0$
1 vote
10
If $\log_{x}y=100$ and $\log_{2}x=10$, then the value of $y$ is : $2^{10}$ $2^{100}$ $2^{1000}$ $2^{10000}$
1 vote
11
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
1 vote
12
The real root of the equation $2^{6x}+2^{3x+2}-21=0$ is $\frac{\log_{2}7}{3}$ $\log_{2}9$ $\frac{\log_{2}3}{3}$ $\log_{2}27$
13
If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to $16/5$ $1$ $24/5$ $47/10$
14
$\frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{50}100}=?$ $1/2$ $0$ $10$ $-4$
15
If $\log_2(5+\log_3a)=3$ and $\log_5(4a+12+\log_2b)=3$, then $a+b$ is equal to $67$ $40$ $32$ $59$
16
If $x$ is a positive quantity such that $2^x=3^{\log_52}$, then $x$ is equal to $1+\log_3\dfrac{5}{3}$ $\log_58$ $1+\log_5\dfrac{3}{5}$ $\log_59$
17
$\log_{12}81=p$, then $3\bigg (\frac{4-p}{4+p}\bigg)$ is equal to $\log_416$ $\log_68$ $\log_616$ $\log_28$
1 vote
18
If $x$ is a real number such that $\log_{3}5=\log_{5}\left ( 2+x \right )$, then which of the following is true? $0<x<3$ $23<x<30$ $x>30$ $3<x<23$
1 vote
19
The value of $\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$ is equal to $1/3$ $2/3$ $5/6$ $7/6$
1 vote
20
If $\log_{10}x-\log_{10}\sqrt x=2 \log_x10$, then a possible value of $x$ is given by $10$ $1/100$ $1/1000$ None of these
21
If $\log_{y}x=\left ( a \cdot \log_{z} y\right ) = \left ( b \cdot \log_{x}z \right )=ab,$ then which of the following pairs of values for $(a,b)$ is not possible? $(-2, 1/2)$ $(1, 1)$ $(\pi , 1/\pi )$ $(2 ,2)$
1 vote
22
Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2}y-\log _{2}x=1-\log_{2}3$. Then $xy$ equals $250$ $25$ $100$ $150$
1 vote
23
If $\log _{x}(a-b)-\log _{x}(a+b)=\log _{x}\left(\dfrac{b}{a}\right)$, find $\dfrac{a^{2}}{b^{2}}+\dfrac{b^{2}}{a^{2}}$. $4$ $2$ $3$ $6$
1 vote
24
If three positive real numbers $a, b$ and $c(c>a)$ are in Harmonic Progression, then $\log\left ( a+c \right )+\log\left ( a-2b+c \right )$ is equal to: $2\:\log\left ( c-b \right )$ $2\:\log\left ( a-c\right )$ $2\:\log\left ( c-a\right )$ $\log\:a+\log\:b+\log\:c$
1 vote
25
If $a=b^{2}=c^{3}=d^{4}$ then the value of $\log_{a}\;(abcd)$ would be $\log_{a}1+\log_{a}2+\log_{a}3+\log_{a}4$ $\log_{a}24$ $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$ $1+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}$
1 vote
26
Difference between (log^2) (n) ,log^2 n, log (log(n)) and (log(n)) ^2?
27
Choose the best alternative If $\log_{7} \log_{5} (x+5x+x)=0$; find the value of $x$. 1 0 2 None of these
28
What is the sum of 'n' terms in the series: $\log m + \log \frac{m^2}{n} + \log \frac{m^3}{n^2} + \log \frac{m^4}{n^3} + \dots + \log \frac{m^n}{n^{n-1}}?$ $\log \left[\frac{n^{n-1}}{m^{(n+1)}} \right]^{\frac{n}{2}}$ $\log \left[\frac{m^m}{n^n} \right]^{\frac{n}{2}}$ $\log \left[\frac{m^{(1-n)}}{n^{(1-m)}} \right]^{\frac{n}{2}}$ $\log \left[\frac{m^{(n+1)}}{n^{(n-1)}} \right]^{\frac{n}{2}}$
29
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by $10$ $\frac{1}{100}$ $\frac{1}{1000}$ None of these
30
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then $\text{M}^9 = \frac{9}{\text{N}}$ $\text{N}^9 = \frac{9}{\text{M}}$ $\text{M}^3 = \frac{3}{\text{N}}$ $\text{N}^9 = \frac{3}{\text{M}}$
31
if $\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to $5$ $4$ $2$ $3$
32
When the curves, $y=\log_{10} x$ and $y=x^{-1}$ are drawn in the $x-y$ plane, how many times do they intersect for values $x \geq 1?$ Never Once Twice More than twice
Let $u=( \log_2 x)^2 – 6 \log_2 x + 12$ where $x$ is a real number. Then the equation $x^u =256$, has no solution for $x$ exactly one solution for $x$ exactly two distinct solutions for $x$ exactly three distinct solutions for $x$
If $x \geq y$ and $y > 1$ then the value of the expression $\log_x\left(\frac{x}{y}\right) + \log_y\left(\frac{y}{x}\right)$ can never be $-1$ $-0.5$ $0$ $1$
If $\log_y x = a \cdot \log_z y = b \cdot \log_x z = ab$ then which of the following pairs of values for $(a,b)$ is not possible? $-2, 1/2$ $1,1$ $0.4, 2.5$ $\pi, 1/\pi$ $2,2$