Logarithm and Antilogarithm Test 18

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Logarithm and Antilogarithm Test 18

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Weekly Quiz Competition

Question 1
1 / -0

Find the value of $${\log_{10} 72} + {\log_{10} {\dfrac{1}{8}}}$$ using log table

A
$$0.903$$

B
$$0.303$$

C
$$0.954$$

D
$$1.234$$

Solution

$$\log_{10}{72}+\log_{10}\left (\dfrac{1}{8} \right )$$
$$=\: \log_{10}{\left (72\times \dfrac{1}{8} \right )}=\log_{10}{9}=\log_{10}{3^{2}}$$
$$=\: 2.\log_{10}{3}=2(0.477)=0.954$$
Question 2
1 / -0

The value of $$\log_{10} 8$$ is equal to

A
$$.903$$

B
$$3.901$$

C
$$.301$$

D
None of the above

Solution

$$\log_{10}8=\log_{10}2^3=3\log_{10}2$$
$$=3\times 0.301$$ $$(\log_{10}2=0.301)$$
$$=0.903$$
Hence, D is the correct option.
Question 3
1 / -0

Find the value of $$\dfrac {\log_{10} 72}{\log_{10} 8}$$ using log table

A
$$\log_{10} 9$$

B
$$1+\dfrac{.954}{.903}$$

C
$$2$$

D
$$\dfrac{.903+.954}{.954}$$

Solution

$$\dfrac{\log_{10}{72}}{\log_{10}{8}}=\dfrac{\log_{10}{(8\times9)}}{\log_{10}{8}}=\dfrac{\log_{10}{8}+\log_{10}{9}}{\log_{10}{8}}$$
$$=1+\dfrac{\log_{10}{3^{2}}}{\log_{10}{2^{3}}}=1+\dfrac{2\log_{10}{3}}{3\log_{10}{2}}$$
$$=1+\dfrac{2.(0.477)}{3.(0.301)}=1+\dfrac{(0.954)}{(0.903)}$$
Question 4
1 / -0

Find the value of $$\log_{10} 72$$ using log table

A
$$0.901+0.909$$

B
$$0.903+0.954$$

C
$$1.890$$

D
$$2.104$$

Solution

$$\log_{10}{72}=\log_{10}(2^{3}.3^{2})$$
$$=\: \log_{10}{2^{3}}+\log_{10}{3^{2}}$$
$$=\: 3.\log_{10}{2}+2.\log_{10}{3}$$
$$=\: 3(0.301)+2(0.4771)$$
$$=\: 0.903+0.954$$
Question 5
1 / -0

If $$\log 625 = k \log 5$$, then the value of $$k$$ is ____

A
$$5$$

B
$$4$$

C
$$3$$

D
$$2$$

Solution

Given, $$\log 625=k \log 5$$

$$\Rightarrow \log (5^4)=k \log 5$$

$$\Rightarrow 4\log 5=k \log 5$$

$$\Rightarrow k=4$$

Option $$B$$ is correct.
Question 6
1 / -0

If $$\dfrac{\log\, x}{l+m-2n} = \dfrac{\log\, y}{m+n-2l} = \dfrac{\log\, x}{n+l-2m}$$, then $$xyz$$ is equal to

A
$$0$$

B
$$lmn$$

C
$$1$$

D
$$2$$

Solution

Let $$\dfrac{\log x}{l+m-2n}=\dfrac{\log y}{m+n-2l}=\dfrac{\log z}{n+l-2m}=k(say)$$

So, we get

$$\log x = k(l+m-2n)$$ ....... $$(i)$$
$$\log y = k(m+n-2l)$$ ....... $$(ii)$$
$$\log z = k(n+l-2m)$$ ....... $$(iii)$$

$$\therefore \log x+\log y + \log z = k(l+m-2n)+k(m+n-2l)+k(n+l-2m)$$
$$\Rightarrow \log x+\log y + \log z = kl+km-2kn+km+kn-2kl+kn+kl-2km$$
$$\Rightarrow \log (xyz) = 0$$

$$\Rightarrow \log xyz = \log 1$$

$$\Rightarrow xyz = 1$$
Question 7
1 / -0

If $$\log_{x} 484 - \log_{x}4 + \log_{x}14641 - \log_{x}1331 = 3$$, then the value of $$x$$ is

A
$$1$$

B
$$3$$

C
$$11$$

D
None of these

Solution

As $$\log_{x} 484 - \log_{x}4 + \log_{x}14641 - \log_{x}1331 = 3$$

$$\Rightarrow \log_{x}\left (\dfrac {484}{4}\right ) + \log_{x} 14641 - \log_{x} 1331 = 3$$

$$\Rightarrow \log_{x} 11^{2} + \log_{x} 11^{4} - \log_{x} 11^{3} = 3$$

$$\Rightarrow (2 + 4 - 3)\log_{x} 11 = 3\Rightarrow \log_{x}11 = 1$$

$$\Rightarrow 11$$

Hence choice (c) is correct.
Question 8
1 / -0

Simplify the following using law of exponents.
$$9^2 \times 9^{18}\times 9^{10}$$

A
$$9^{30}$$

B
$$9^{25}$$

C
$$9^{15}$$

D
$$9^{10}$$

Solution

We know that,

$$a^{m}\times a^{n}\times a^{p}=a^{m+n+p}$$

Therefore,

$$9^{2}\times 9^{18}\times 9^{10}=9^{2+18+10}$$

$$=9^{30}$$
Question 9
1 / -0

The value of $$[2-3(2-3)^{-1}]^{-1}$$ is __________.

A
$$\displaystyle\frac{-1}{5}$$

B
$$\displaystyle\frac{1}{5}$$

C
$$-5$$

D
$$5$$

Solution

$$=$$$$[2-3(2-3)^{-1}]^{-1}$$
$$=$$$$[2-3(-1)^{-1}]^{-1}$$
$$=$$$$[2-3(-1)]^{-1}$$
$$=$$$$[2+3]^{-1}$$
$$=$$$$\dfrac{1}{5}$$
Question 10
1 / -0

Which of the following values are equal?
(P) $$1^{4}$$ (Q) $$4^{\circ}$$ (R) $$0^{4}$$ (S) $$4^{1}$$.

A
$$P$$ and $$Q$$

B
$$Q$$ and $$R$$

C
$$P$$ and $$R$$

D
$$P$$ and $$S$$

Solution

(P) $$1^{4} = 1$$
(Q) $$4^{0} = 1$$
(R) $$0^{4} = 0$$
(S) $$4^{1} = 4$$

Hence, $$P$$ and $$Q$$ are equal.

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Logarithm and Antilogarithm Test 18

Result

Logarithm and Antilogarithm Test 18

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SHARING IS CARING

Question 1

$$0.903$$

$$0.303$$

$$0.954$$

$$1.234$$

Solution

Question 2

$$.903$$

$$3.901$$

$$.301$$

None of the above

Solution

Question 3

$$\log_{10} 9$$

$$1+\dfrac{.954}{.903}$$

$$2$$

$$\dfrac{.903+.954}{.954}$$

Solution

Question 4

$$0.901+0.909$$

$$0.903+0.954$$

$$1.890$$

$$2.104$$

Solution

Question 5

$$5$$

$$4$$

$$3$$

$$2$$

Solution

Question 6

$$0$$

$$lmn$$

$$1$$

$$2$$

Solution

Question 7

$$1$$

$$3$$

$$11$$

None of these

Solution

Question 8

$$9^{30}$$

$$9^{25}$$

$$9^{15}$$

$$9^{10}$$

Solution

Question 9

$$\displaystyle\frac{-1}{5}$$

$$\displaystyle\frac{1}{5}$$

$$-5$$

$$5$$

Solution

Question 10

$$P$$ and $$Q$$

$$Q$$ and $$R$$

$$P$$ and $$R$$

$$P$$ and $$S$$

Solution

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