Properties of Logarithms

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. 0

2. $\frac{23}{17}$

3. $\frac{17}{8}$

4. 1

Q.

The Process of Verifying the Identity of a User Is Called :

1. Authentication

2. Identification

3. Validation

4. Verification

Q.

Which of the following is essential concept related to cloud?

1. Abstraction

2. Productivity

3. Reliability

4. All of these

Q.

If $log\frac{x}{y}+log\frac{y}{x}=log(x+y)$, then which of the following equations is true?

1. $x+y=1$

2. $x-y=1$

3. $x+y=0$

4. $x^2+y^2=1$

Q.

The value of the expression $2log3-\frac{1}{2}log16+log12$ is equal to ___

1. $log13$

2. $log27$

3. $log72$

4. $log36$

Q.

Role based authentication is done using _____ setting.

Q.

If $lo{g}_{10}2=0.30103$, then $lo{g}_{10}50=$

1. 2.30103

2. 1.69897

3. 0.69897

4. 2.69897

Q.

If ${\log }_{a}x$ can be written as $\frac{p}{q}$; where p and q are prime to each other, then ${\log }_{a}x$ is a/an _____.

1. Integer

2. natural number

3. whole number

4. rational number

Q.

Evaluate $lo{g}_{10}\frac{1}{10000}$.

1. -4

2. 4

3. 1

4. -1

Q. ${\log }_{10}(x+1)+lo{g}_{10}(x-1)=lo{g}_{10}11+2lo{g}_{10}3$
The value of x is .

1. 10
2. $2{\log }_{10}3$
3. ${\log }_{10}2$

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. If log2x=0 , then x =

1. 1
2. -1
3. 0

Q. Sort the following in increasing order.

1. ${\log }_2\left(8\right)$
2. ${\log }_3\left(81\right)$
3. ${\log }_{10}\left(100000\right)$
4. ${\log }_2\left(64\right)$

Q. Match the following with the correct value of x in each of the below cases.

1. 7
2. 8
3. 3
4. 64

Q. If $A=lo{g}_{2}lo{g}_{2}lo{g}_{4}256+2lo{g}_{\sqrt{2}}2$, then A is equal to

1. 2
2. 3
3. 5
4. 7

Q. $7log\left(\frac{16}{15}\right)+5log\left(\frac{25}{24}\right)+3log\left(\frac{81}{80}\right)$ is equal to -

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

Q.

$\text{Find}x\text{if}$ $lo{g}_{10}(x+1)+lo{g}_{10}(x-1)=lo{g}_{10}11+2lo{g}_{10}3$

1. 10

2. 100

3. 1

4. 2

Q.

$\text{Solve for}x\text{in the equation}$ $log\left[log\right(2+lo{g}_2(x+1)\left)\right]=0$

1. $2^2-1$

2. $2^8-1$

3. $2^8$

4. $3^8-1$

Q.

log(x-y)=logx-logy

1. True

2. False

Q. If $lo{g}_{10}x=ythenlo{g}_{1000}{x}^2$ is equal to

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

Q. The value of ${\log }_{e}144$ is.

1. $2{\log }_{e}12$
2. $4{\log }_{e}2$
3. ${\log }_{e}3$

Q. ${\log }_{10}5+{\log }_{10}8-2{\log }_{10}2$ =

1. 4
2. ${\log }_{10}2$
3. 1

Q.

Divide a $5inch$ line into two parts so that one part is:

(a) $2\frac{1}{4}inches$shorter than the other;

(b) $3$ times the other.

Q.

Which of the following statements are correct?

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

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

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

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

Q.

Simplify $7log\left(\frac{32}{15}\right)+5log\left(\frac{25}{24}\right)+3log\left(\frac{81}{160}\right)$

1. $5log2$

2. $log2$

3. $log3$

4. 1

Q. Find the value of $lo{g}_{\sqrt{3}}405-lo{g}_{\sqrt{3}}135+lo{g}_{3}9$