Logarithms

Q. $23.\overline{43}$ when expressed in the form $\frac{p}{q}$(p, q are integers q ≠ 0), is

(a) $\frac{2320}{99}$

(b) $\frac{2343}{100}$

(c) $\frac{2343}{999}$

(d) $\frac{2320}{199}$

Q.

The population of a town is increasing at the rate of 5% p.a. What will be the population of the town after 2 years, if the present population is 16, 000?

1. 17, 000

2. 18, 640

3. 17, 640

4. 14, 512

Q.

The number of non-empty subsets of the set $\{1,2,3,4\}$ is

1. $15$

2. $14$

3. $16$

4. $17$

Q.

If $\log 4=0.6020$, then find the value of $\log 80$.

Q.

What is the value of $lo{g}_{\frac{1}{3}}9\sqrt{3}$

1. $\frac{2}{5}$

2. $\frac{5}{2}$

3. $\frac{-2}{5}$

4. $\frac{-5}{2}$

Q.

It is given that $\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+....=\frac{{\pi }^4}{90}$. Then $\frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+...$is equal to

1. $\frac{{\pi }^4}{96}$

2. $\frac{{\pi }^4}{45}$

3. $\frac{89\pi }{90}$

4. None of these

Q.

In a factory, the production of tyres rose to 484000 from 400000 in 2 years. Find the rate of growth p.a.

1. 11%

2. 5%

3. 8%

4. 10%

Q.

The population of a city continuously grows at a rate of 8% yearly. About how many years will it take for the population to triple?

1. 12

2. 10

3. 14

4. 11

Q.

A group of researchers were given an assignment to collect different types of leaves. The group collected 256 types of leaves. Represent the number of leaves collected in the form of exponential expression with its base being indivisible. [2 MARKS]

Q.

Express $x^{\frac{3}{4}}({\log }_{3}x{)}^2+{\log }_{3}x-\frac{5}{4}=\sqrt{3}$​ in terms of t where t = ${\log }_3$ x.

1. + 7t + 2 = 0

2. + + 9t + 2 = 0

3. + - 5t - 2 = 0

4. + - 5t - 2 = 0

Q.

Question 161

Shikha has an order from a golf course designer to put palm trees through
a $(\times 2^3)$ machine and then through $a(\times 3^3)$ machine. She thinks that she can do the job with a single repeater machine. What single repeater machine she should use?

Q. If $x^2+y^2=25xy,$then prove that $2\log (x+y)=3\log 3+\log x+\log y.$

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

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

Q.

standerd form of-51/84

Q.

If $\frac{lo{g}_2(4x^2-x-1)}{lo{g}_2(x^2+1)}>1$ then x lies in the interval

1. $(-\infty ,-2/3)$
   

2. $(1,\infty )$
   

3. $(-2/3,0)$
   

4. None of these

Q.

Write 5⁴5 = 2502 in logarithmic form

1. log₅4 = 2502

2. log₅4 = 2502

3. log₄5 = 2502

4. log₅2502 = 4

Q.

Evaluate $\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}$

Q. If A and B are any two empty sets and A is a proper subset of B. If cardinal number of A is 5 then minimum possible value of n (A Delta B) is

Q. The set of all $x$ satisfying $4^{x^2+2}-9\times 2^{x^2+2}+8=0$ consists of

1. Infinitely many points,
2. Finitely many points from the set of all natural numbers,
3. Finitely many points from the set of all integers
4. Two integers

Q. Express ${\log }_{100}0.1=-\frac{1}{2}$ in exponential form:

Q.

Express $log135$ in terms of $m$ and $n$ if $m=log15$ and $n=log3$.

1. $2mn$

2. $m+2n$

3. $2m+n$

4. $m+n$

Q.

If $lo{g}_{x}y=100$ and $lo{g}_{2}x=10$, then the value of y is

1. ${1000}^2$

2. $2^{100}$

3. $2^{1000}$

4. $2^{10000}$

Q.

If $lo{g}_{10}x=y$. Then,

1. $lo{g}_{10}{x}^2=y^2$

2. $lo{g}_{10}{x}^2=2y$

3. $lo{g}_{1000}{x}^2=\frac{3y}{2}$

4. $lo{g}_{1000}{x}^2=\frac{2y}{3}$

Q.

Which is the correct order for a given number $\alpha$ in increasing order?

1. $lo{g}_2\alpha ,lo{g}_3\alpha ,lo{g}_e\alpha ,lo{g}_{10}\alpha$

2. $lo{g}_{10}\alpha ,lo{g}_3\alpha ,lo{g}_e\alpha ,lo{g}_2\alpha$

3. $lo{g}_{10}\alpha ,lo{g}_e\alpha ,lo{g}_2\alpha ,lo{g}_3\alpha$

4. $lo{g}_3\alpha ,lo{g}_e\alpha ,lo{g}_2\alpha ,lo{g}_{10}\alpha$

Q. Solve the following inequality:
$\frac{x^4-3x^3+2x^2}{x^2-x-30}>0$

Q.

Solution set of the inequality
$\frac{1}{2^x-1}>\frac{1}{1-2^{x-1}}is$

1. $(0,lo{g}_2(4/3\left)\right)$

2. $(-1,\infty )$

3. $(1,\infty )$

4. $(0,lo{g}_2(4/3\left)\right)\cup (1,\infty )$

Q.

If n! =840*4320, then find the value of n.

Q.

The set of real values of x satisfying the equation
${|x-1|}^{lo{g}_3\left(x^2\right)-2lo{g}_x\left(9\right)}=(x-1{)}^7$
is

1. {2}
   

2. {27, 81}
   

3. {2, 81}

4. {81}
   

Q. Find $x\in R$

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

Q.

The set of real values of x satisfying the equation
${|x-1|}^{lo{g}_3\left(x^2\right)-2lo{g}_x\left(9\right)}=(x-1{)}^7$
is

1. {2}
   

2. {27, 81}
   

3. {81}
   

4. {2, 81}