Natural Logarithm

Q. If any number divided by zero is infinity and
if zero divided by any number is 0 then

What is 0/0????
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Q.

List of formulas of number system

Q.

write in ascending order

2^60, 3^48, 4^36, 5^24

Q.

The logarithm of a negative number is obtained by multiplying its magnitude with -1. State true or false.

1. 2 log_e 12

2. 4 log_e 2+2 log_e 3

Q.

Logarithms with the base of e are called

1. natural logarithms

2. common logarithms

Q. If $\frac{loga}{b-c}=\frac{logb}{c-a}=\frac{logc}{a-b}$, then find the value of $a^a.b^b.c^c$

1. 1

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

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

Q.

If log a + log b = log c then a = _______ .

1. ab = c

2. ab = log c

3. a + b = c

4. a = bc

Q.

The definition of a logarithm indicates that it is related to exponents.

1. True

2. False

Q. If ${\log }_{k}x.{\log }_{5}k={\log }_{x}5,k\ne 1,k>0$, then the value of $x$ is equal to

1. $k$
2. $5$
3. $\frac{1}{5}$
4. none of these

Q. If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$

Q. Define logarithm and write down different properties.

Q. If $a^x=b^y=c^z$ and $b^2=ac$, find $\frac{1}{x}+\frac{1}{z}-\frac{2}{y}$

Q. If $\frac{logx}{b-c}=\frac{logy}{c-a}=\frac{logz}{a-b}$, then what is the value of xyz?

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

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

Q. The value of $\left({\log }_{3}11\right)\left({\log }_{11}13\right)\left({\log }_{13}15\right)\left({\log }_{15}27\right)\left({\log }_{27}81\right)$ is equal to

1. $3$
2. $2$
3. $1$
4. $4$

Q. If $\frac{logx}{b-c}=\frac{logy}{c-a}=\frac{logz}{a-b}$, then what is the value of xyz?

1. 1

Q.

Express the following as decimals.

$3\times 10+4\times 1+7\times \frac{1}{10}$

Q. Write the following in logarithm form:
${10}^{-3}=0.001$

Q. Evaluate $\underset{1}{\overset{2}{\int }}\log xdx.$

Q. If $\frac{logx}{b-c}=\frac{logy}{c-a}=\frac{logz}{a-b}$, then what is the value of xyz?

Q. Find the value of $7\log \left(\frac{16}{15}\right)+5\log \left(\frac{25}{24}\right)+3\log \left(\frac{81}{80}\right)$

1. $\log 2$
2. $\log 4$
3. $\log 15$
4. $\log 9$

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

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