Fundamental laws of logarithms

Q.

If p is $30\%$more than q, then find $\frac{\mathrm{p}}{\mathrm{p}-\mathrm{q}}$

Q. If $x^a=y,y^b=z,z^c=x$ then, abc=

1. xyz
2. 1
3. 0
4. 2

Q. The value of
$lo{g}_{3}2lo{g}_{4}3lo{g}_{5}4\dots lo{g}_{15}14lo{g}_{16}15$ is

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. 1

Q.

Factor out the coefficient of the variable term.

$\frac{1}{7}a+\frac{1}{7}$

Q.

Factor out the coefficient of the variable term.

$\frac{5}{2}k-2$

Q. If a and b are positive real numbers such that 2 log (3a - 2b) = log a + log b, then the value of $\frac{a}{b}$=

1. $1$
2. $\frac{2}{3}$
3. $\frac{4}{9}$
4. $2$

Q. If $lo{g}_{k}A.lo{g}_{5}k=3$, then A=

1. 243
2. $k^3$
3. $5k^3$
4. 125

Q. The value of $(0.05{)}_{\sqrt{20}}^{log}(0.1+0.01+0.001+.....)$

1. $81$
2. $\frac{1}{81}$
3. $20$
4. $\frac{1}{20}$

Q.

Factor out the coefficient of the variable term.

$\frac{1}{4}y+\frac{3}{8}$

Q.

If $(3x{)}^{log3}=(4y{)}^{log4}$ and $(4{)}^{logx}=(3{)}^{logy}$, then x equals

1. 1/3
   

2. 1/2
   

3. 1/4
   

4. 7

Q. $lo{g}_{10}tan{1}^{\circ }+lo{g}_{10}tan{2}^{\circ }+\dots lo{g}_{10}tan{89}^{\circ }$

1. 0
2. 1
3. 3
4. 2

Q. The value of $lo{g}_{b}a.lo{g}_{c}b.lo{g}_a$ c is

1. log abc
2. 0
3. 1
4. 10

Q. $log\{lo{g}_{ab}a+\frac{1}{lo{g}_{b}ab}\}=$

1. 0
2. 1
3. log ab
4. None of these

Q. The value of $\sqrt{\left(lo{g}_{0.5}^{2}4\right)}$ is

1. -2
2. $\sqrt{(-4)}$
3. 2
4. None of these

Q. If $\frac{loga}{b-c}=\frac{logb}{c-a}=\frac{logc}{a-b}$ then $a^a.b^b.c^c=$

1. 2
2. -1
3. None of these
4. 1

Q.

If $lo{g}_2(4^{x+1}+4)lo{g}_2(4^x+1)=lo{g}_{2}8,$ then x equals

1. -1
   

2. 0
   

3. 1
   

4. 2

Q. $\frac{lo{g}_{8}17}{lo{g}_{9}23}-\frac{lo{g}_{2\sqrt{2}}17}{lo{g}_{3}23}$ is equal to

1. 1
2. $\frac{17}{8}$
3. $\frac{23}{17}$
4. 0

Q. The value of $2^{lo{g}_{3}5}-5^{lo{g}_{3}2}$ is

1. 0
2. 3
3. 5
4. 2

Q.

Factor out the coefficient of the variable term.

$\frac{1}{2}q+\frac{5}{2}$

Q. If $lo{g}_{7}2=m,thenlo{g}_{49}28$ is equal to

1. $2(1+2m)$
2. $\frac{1+2m}{2}$
3. $\frac{2}{1+2m}$
4. $1+m$

Q. If $\frac{1}{lo{g}_{a}x}+\frac{1}{lo{g}_{c}x}=\frac{2}{lo{g}_{b}x}$, then a, b, c are in

1. A.P.
2. G.P.
3. H.P.
4. None of these

Q. If $lo{g}_a\left(ab\right)=x$, then $lo{g}_b\left(ab\right)$ is equal to

1. $\frac{1}{x}$
2. $\frac{x}{1+x}$
3. $\frac{x}{x-1}$
4. $\frac{x}{1-x}$

Q. $\frac{1}{lo{g}_{xy}xyz}+\frac{1}{lo{g}_{yz}xyz}+\frac{1}{lo{g}_{zx}xyz}=$

1. 0
2. 1
3. 2
4. $lo{g}_{zx}xyz$

Q.

$\sqrt{lo{g}_{2}x}-0.5=lo{g}_2\sqrt{x}$, then x equals

1. 4
   

2. 16
   

3. 8
   

4. None of these

Q. If a, b, c are in G.P., then $lo{g}_{a}n,lo{g}_{b}n,lo{g}_{c}n$ are in

1. G.P.
2. H.P.
3. None
4. A.P.

Q. If $lo{g}_{10}2=0.30103,lo{g}_{10}3=0.47712$, the number of digits in $3^{12}\times 2^8$ is

1. 7
2. 8
3. 9
4. 10

Q. If a, b, c are distinct positive numbers each different from 1 such that
$[lo{g}_{b}alo{g}_{c}a-lo{g}_{a}a]+[lo{g}_{a}blo{g}_{c}b-lo{g}_{b}b]+[lo{g}_{a}clo{g}_{b}c-lo{g}_{c}c]=0$ then abc

1. 1
2. 2
3. 3
4. None