Representation of Logarithmic Function

Q.

In the exponential growth equation $N_t=N_0{e}^{rt}$, e represents:

1. The base of number logarithms

2. The base of exponential logarithms

3. The base of geometric logarithms

4. The base of natural logarithms

Q.

How do you write $0.0001$ in scientific notation?

Q.

If log 2 = 0.3010 and log 3 = 0.4771, find the value of $log\sqrt{24}$

1. 0.69005

2. 0.605

3. 1.69005

4. 0.79005

Q. If $lo{g}_{10}3=0.477$, the number of digits in $3^{40}$ is

1. 19
2. 20
3. 21
4. 18

Q.

The approximate value of $\sqrt[5]{33}$ correct to $4$decimal

1. $2.0000$

2. $2.1001$

3. $2.0125$

4. $2.0500$

Q.

Express $lo{g}_{10}\sqrt[5]{5108}$ in terms of $lo{g}_{10}2$ and $lo{g}_{10}3$

1. $\frac{1}{5}2lo{g}_{10}2+3lo{g}_{10}3$

2. $\frac{1}{5}2lo{g}_{10}4+3lo{g}_{10}3$

3. $\frac{1}{5}2lo{g}_{10}2+lo{g}_{10}3$

4. $\frac{1}{5}lo{g}_{10}2+3lo{g}_{10}3$

Q.

$\frac{log\sqrt{27}}{log27}$ is equal to

1. $\frac{1}{9}$

2. $\frac{1}{\sqrt{27}}$

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

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

Q. Prove that $7\log \frac{16}{15}+5\log \frac{25}{24}+3\log \frac{81}{80}=\log 2$

Q.

Find the value of ${27}^{\left(\frac{1}{{\log }_{4}3}\right)}+{16}^{{\log }_{4}2}+3^{\left(\frac{4}{{\log }_{7}9}\right)}$

1. 64

2. 68

3. 117

4. 49

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. A.P.

2. G.P.

3. None

4. H.P.

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

1. 2.69897
2. 1.69897
3. 2.30103
4. 0.69897

Q. Given:$\log 2=0.3010$ and $\log 3=0.4771$, find the value of $\log \sqrt{18}$.

Q.

If $lo{g}_{10}4=0.602$, then $lo{g}_{4}10=0.301$

1. False

2. True

Q.

The value of $\frac{1}{lo{g}_{2}30}+\frac{1}{lo{g}_{3}30}+\frac{1}{lo{g}_{5}30}$ is

1. 0

2. 1

3. 5

4. 30

Q.

$lo{g}_{x}x=0$

1. True

2. False

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

1. 1.69897
2. 0.69897
3. 2.30103
4. 2.69897

Q. Solve:$\sqrt{\frac{{\log }_2\left(x-2\right)}{{\log }_{1/2}\left(3x-1\right)}}=1$

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 ${\log }_{1/\sqrt{2}}\left(1/\sqrt{8}\right)={\log }_2(4^x+1).{\log }_2(4^{x+1}+4)$, then $x=$.................

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

Q.

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

Q.

$lo{g}_{5}a.lo{g}_{a}x=2$, then $x$ is equal to

1. 125

2. 25

3. None of these

4. $a^2$

Q. If $x=lo{g}_{b}a,y=lo{g}_{c}b,z=lo{g}_{a}c$, then xyz is

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

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

Q. The first term of an A.P is $\log a$ and the second term is $\log b$. Express the sum to $n$ terms as a logarithm.

1. $\log {\left(\frac{b^{n-1}}{a^{n-3}}\right)}^{n/2}$
   
2. $\log \left(\frac{b^{n-1}}{a^{n-3}}\right)$
   
3. $\log {\left(\frac{b^{n-1}}{a^{n-3}}\right)}^n$
4. $\log {\left(\frac{b^{n-3}}{a^{n-1}}\right)}^{n/2}$

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

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

Q. ${\log }_{10}8+{\log }_{10}5-{\log }_{10}4=$

1. ${\log }_{10}36$
2. ${\log }_{10}9$
3. $1$
4. $-1$

Q. If $l=\log \frac{5}{7},m=\log \frac{7}{9}$ and $n=2(\log 3-\log \sqrt{5});$ then the value of $l+m+n$ will be

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

Q.

___________is the only non zero whole number which when multiplied by itself , gives the product equal to the number itself .

Q. $x^{{\log }_{5}x}>5$ implies:

1. $x\in (0,\infty )$
2. $x\in (0,\frac{1}{5})\cup (5,\infty )$
3. $x\in (1,\infty )$
4. $x\in (1,2)$

Q. If ${\log }_{125}p=\frac{1}{6}$, then find the value of $p$.