Logarithm and Antilogarithm Test 13

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Logarithm and Antilogarithm Test 13

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Weekly Quiz Competition

Question 1
1 / -0

Find the mantissa of the logarithm of the number $$0.002359$$.

A
$$3710$$

B
$$3718$$

C
$$3728$$

D
$$3742$$

Solution

We have to find $$\log (0.002359)$$
Firstly, we will write $$0.002359$$ in standard form.
So, $$0.002359 = 2.359 \times 10^{-3}$$
Here, characteristic is -3.

To find the mantissa of $$\log (0.002359)$$, we first look in the row starting with 23. In this row, look at the number in the column headed by 5. The number is 3711.

Now, move to the column of mean differences and look under the column headed by 9 in the row corresponding to 23. We see the number 17 here.

Add this number to 3711. We get the number 3728. This is the required mantissa of $$\log (0.002359)$$.

Mantissa of $$\log 23.598$$, $$\log 2.3598$$ and 0.023598 is the same (only characteristics are different).
Question 2
1 / -0

If $$\displaystyle \frac {\log 81}{\log 27} = x$$ and $$x$$ is expressed as $$\displaystyle 1 \frac {1}{m}$$, then $$m$$ is equal to

A
$$2$$

B
$$1$$

C
$$0$$

D
$$3$$

Solution

$$\displaystyle \frac {\log 81}{\log 27} = x$$
$$\displaystyle \Rightarrow x = \dfrac {\log 3^4}{\log 3^3} = \dfrac {4 \log \: 3}{3 \log 3} = \dfrac {4}{3} = 1 \dfrac {1}{3}$$
$$ \therefore m =3$$
Question 3
1 / -0

The logarithm form of $$\displaystyle 5^3 = 125$$ is equal to

A
$$\displaystyle \log_5 125 = 3$$

B
$$\displaystyle \log_5 125 = 5$$

C
$$\displaystyle \log_3 125 = 5$$

D
$$\displaystyle \log_5 3 = 3$$

Solution

Since, $$5^3=125$$
$$\implies \log$$ of $$125$$ to base $$5$$ is $$3$$
$$\implies \log_5 125 = 3$$
Question 4
1 / -0

If $$\displaystyle \frac {\log 128}{\log 32} = x$$, then the value of $$x$$ will be

A
$$\dfrac{5}{7}$$

B
$$\dfrac{7}{5}$$

C
$$\dfrac{8}{5}$$

D
$$\dfrac{5}{8}$$

Solution

Given, $$\displaystyle \frac {\log 128}{\log 32} = x $$
$$\Rightarrow \dfrac{\log2^7}{\log2^5}=x$$
$$ \Rightarrow \dfrac{7\log2}{5\log2}=x$$ (Using $$\log a^b=b\log a$$)
$$\therefore x = \dfrac{7}{5}$$.
Question 5
1 / -0

If $$\displaystyle \log_x 2 = -1$$, then the value of $$x$$ is equal to

A
$$2$$

B
$$\dfrac{1}{2}$$

C
$$-2$$

D
$$1$$

Solution

Since, $$ \log _{ x }{ 2 } =-1$$
$$\implies 2= { x }^{ -1 }$$
$$\implies 2 = \dfrac{1}{x}$$
$$\implies x = \dfrac{1}{2}$$.
Question 6
1 / -0

Given $$\displaystyle 3^{x} = \frac {1}{9}$$ then $$x=?$$

A
$$-1$$

B
$$-2$$

C
$$1$$

D
$$2$$

Solution

Since, $$3^{-2}=\dfrac{1}{9}$$
$$\implies \log$$ of $$\dfrac{1}{9}$$ to base $$3$$ is $$-2$$
$$\implies \log_3\dfrac{1}{9}= -2$$.
Question 7
1 / -0

If $$\displaystyle \frac {\log 225}{\log 15} = \log x$$, then the value of $$x$$ is equal to

A
$$400$$

B
$$300$$

C
$$200$$

D
$$100$$

Solution

Given, $$\displaystyle \frac {\log 225}{\log 15} = \log x$$
$$\implies \dfrac{\log 15^2}{\log 15}=\log x$$
$$\implies \dfrac{2\log 15}{\log 15}=\log x$$ (Using $$\log a^b=b\log a$$)
$$\implies \log x= 2$$
$$\implies \log x= \log 100$$
$$\implies x=100$$.
Question 8
1 / -0

If $$\displaystyle \log_{10} 8 = 0.90$$, then the value of $$\displaystyle \log_{10}0.125$$ is

A
$$0.9$$

B
$$1$$

C
$$0$$

D
$$-0.9$$

Solution

$$\log_{10}8 = 0.90$$
$$\log_{10}0.125 = \log_{10} \dfrac{1}{8} = \log_{10} 8^{(-1)} =-\log_{10}8 = -0.9$$ (Using $$\log a^b = b \log a$$)
Question 9
1 / -0

The value of $$\displaystyle \log (a)^3 \div \log a$$ is equal to

A
$$1$$

B
$$4$$

C
$$6$$

D
$$3$$

Solution

Let, $$x = \log (a)^3 \div \log a$$
$$\therefore x = \dfrac{3\log a}{\log a} = 3$$ (Using $$\log a^b = b \log a $$)
Question 10
1 / -0

If $$\log_{10} x = 2a$$ and $$\displaystyle \log_{10} y = \dfrac {b}{2}$$, then $$\displaystyle 10^{2b + 1}$$ in terms of $$y$$ is $$\displaystyle my^4$$. Then what is the value of $$m$$?

A
$$13$$

B
$$15$$

C
$$10$$

D
$$5$$

Solution

Since, $$ \log _{ 10 }{ x } = a$$ and $$ \log _{ 10 }{ y } = \dfrac { b }{ 2 } $$
$$\implies x = { 10 }^{ a }$$ and $$ y={ 10 }^{ \dfrac { b }{ 2 } }$$
Consider, $${ 10 }^{ 2b+1 } $$
$$= { 10 }^{ 2b } \cdot 10$$
$$= { 10 }^{ 4(\dfrac { b }{ 2 } ) } \cdot 10$$
$$= { y }^{ 4 } \cdot 10 $$
Hence, C will be correct answer.

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Logarithm and Antilogarithm Test 13

Result

Logarithm and Antilogarithm Test 13

Score

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Rank

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SHARING IS CARING

Question 1

$$3710$$

$$3718$$

$$3728$$

$$3742$$

Solution

Question 2

$$2$$

$$1$$

$$0$$

$$3$$

Solution

Question 3

$$\displaystyle \log_5 125 = 3$$

$$\displaystyle \log_5 125 = 5$$

$$\displaystyle \log_3 125 = 5$$

$$\displaystyle \log_5 3 = 3$$

Solution

Question 4

$$\dfrac{5}{7}$$

$$\dfrac{7}{5}$$

$$\dfrac{8}{5}$$

$$\dfrac{5}{8}$$

Solution

Question 5

$$2$$

$$\dfrac{1}{2}$$

$$-2$$

$$1$$

Solution

Question 6

$$-1$$

$$-2$$

$$1$$

$$2$$

Solution

Question 7

$$400$$

$$300$$

$$200$$

$$100$$

Solution

Question 8

$$0.9$$

$$1$$

$$0$$

$$-0.9$$

Solution

Question 9

$$1$$

$$4$$

$$6$$

$$3$$

Solution

Question 10

$$13$$

$$15$$

$$10$$

$$5$$

Solution

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