Standard Logarithm

Q.

What is the formula of $\begin{array}{rcl}& & {}_n{}^{n}C\end{array}$?

Q.

Find the value of ${\log }_2.{\log }_3.........{\log }_{100}.100.99.98..............2.1$

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Q.

If $lo{g}_{3}x=a$, find the value of ${81}^{a-1}$ in terms of x.

Q.

Prove that

$\left(i\right)log12=log3+log4$

$\left(ii\right)log50=log2+2log5$

$\left(iii\right)log(1+2+3)=log1+log2+log3$

Q.

Find the value of ${\log }_e$ 144.

1. 4 log_e 2+2 log_e 3

2. 2 log_e 12

3. log_e 2 + log_e 18

4. All of these

Q. Sort the following in the descending order of their values.

1. 27log35
2. 4log27
3. 91+log34
4. 251+log52

Q.

Find the value of $5^{{\log }_5{9}^2}$

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Q.

Express each of the following in exponential form:

$\left(i\right)lo{g}_{2}64=6$

$\left(ii\right)lo{g}_{10}0.01=-2$

Q.

Find the value of ${\log }_2.{\log }_{3}9$

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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 ${(\frac{3}{2}{x}^2-\frac{1}{3x})}^9$ is expanded in descending powers of x, then $7^{th}$ term is given by:

1. 7/18

2. 16x/27

3. 16/27

4. -(7x/18)

Q. ${\log }_{e}121$ =

1. $2{\log }_{e}11$
2. $11{\log }_{e}11$
3. ${\log }_{e}100+21$

Q. ${\log }_{2}7$ is a/an

1. natural number
2. integer
3. irrational number
4. rational number

Q.

2 lines originating from a point P intersects a circle at 4 points as shown in the figure.Given AB=5, AP=2, PC=1; what is the length of CD.

1. 11

2. 13

3. 10

4. 3

Q. The value of $3^{\sqrt{{\log }_{3}4}}$ is equal to

1. $3^{\sqrt{{\log }_{4}3}}$
2. $4^{\sqrt{{\log }_{4}3}}$
3. $4^{\sqrt{{\log }_{3}4}}$
4. $0$

Q.

$a^{lo{g}_a^m}=m$ $\{a,m>anda\ne 1\}$

1. True

2. False

Q. If $\log (x^2-21)=2$, then the value $x$ will be

1. $13$
2. $-17$
3. $-11$
4. $12$

Q. x² e^x log x

Q. If a, b, c are positive real numbers such that $a^{lo{g}_{3}7}=27;b^{lo{g}_{7}11}=49$ and $c^{lo{g}_{11}25}=\sqrt{11}$. The value of $(a^{(lo{g}_{3}7{)}^2}+b^{(lo{g}_{7}11{)}^2}+c^{(lo{g}_{11}25{)}^2})$ equals

1. $489$
2. $400$
3. $464$
4. $469$

Q.

The number ${\log }_{2}7$ is _____

1. a natural number

2. a rational number

3. an irrational number

4. a negative integer

Q. If $a^2+4b^2=12ab$, then log(a + 2b) is

1. $\frac{1}{2}[loga+logb-log2]$
2. $log\frac{a}{2}+log\frac{b}{2}+log2$
3. $\frac{1}{2}[loga+logb+4log2]$
4. $\frac{1}{2}[loga-logb+4log2]$

Q.

If $y=2^{\frac{1}{{\log }_{x}4}}$. Then

1. $y=x$

2. $y=x^2$

3. $y=x^{\frac{1}{2}}$

4. $y=x^3$

Q. Determine the value of the following
${\log }_{\frac{2}{3}}\frac{8}{27}$

Q.

Find the value of ${\log }_2.{\log }_{3}9$

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