Property 2

Q.

log (a - b) = log a - log b. State whether true or false.

1. True

2. False

Q. Express $0.6+0.\overline{7}+0.4\overline{7}$ In the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Q.

log ( 5 $\times$ 10) = log (5 +10). State whether true or false.

1. True

2. False

Q. If $lo{g}_{4}5$ = a and $lo{g}_{5}6$ = b, then $lo{g}_{3}2$ is equal to

1. $\frac{1}{2a+1}$
2. $\frac{1}{2b+1}$
3. $2ab+1$
4. $\frac{1}{2ab-1}$

Q. If $lo{g}_{4}5=a$ and $lo{g}_{5}6=b$, then, $lo{g}_3$ 2 is equal to

1. $\frac{1}{2a+1}$
2. $\frac{1}{2b+1}$
3. $2ab+1$
4. $\frac{1}{2ab-1}$

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

1. $0$
2. $logab$
3. $Noneofthese$
4. $1$

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

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

Q. If $lo{g}_{4}5$ = a and $lo{g}_{5}6$ = b, then $lo{g}_{3}2$ is equal to

1. $\frac{1}{2a+1}$
2. $\frac{1}{2b+1}$
3. $\frac{1}{2ab-1}$
4. $2ab+1$

Q.

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

1. 0

2. $log\left(abc\right)$

3. $lo{g}_{a}a$

4. 1

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

1. 0
2. $log\left(abc\right)$
3. $lo{g}_{a}a$
4. 1

Q.

Which of the following statements are correct?

1. $log\left(2\right)\times log\left(4\right)=log(4\times 2)$

2. $lo{g}_{3}3=1$

3. $lo{g}_{10000}1=0$

4. $log1+log2+log3=log(1+2+3)$

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

1. $0$
2. $1$
3. $Noneofthese$
4. $logab$

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

1. 0
2. $log\left(abc\right)$
3. $lo{g}_{a}a$
4. 1

Q. ${\log }_{10}5+{\log }_{10}2=1$

1. True
2. False

Q. If $\log 4+2\log 3$ is $\log m$, then value of $m$ is equal to

1. $33$
2. $31$
3. $36$
4. $38$

Q. Evaluate
${\int }_1^3(4x+\frac{1}{x}+1)dx$

Q. Find the value of ${[{\left(\frac{1}{3}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}]}^{-1}$

1. $1$
2. $-1$
3. $0$
4. $-12$

Q.

$lo{g}_{e}x$ is defined for all non-negative values of $x$

1. True

2. False