Logarithm and Antilogarithm Test 10

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Logarithm and Antilogarithm Test 10

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Weekly Quiz Competition

Question 1
1 / -0

$$\log {28}$$ is same as_____

A
$$\log {16} +\log {12}$$

B
$$\log {15} + \log {13}$$

C
$$\log {2} + \log {14}$$

D
$$\log {26} + \log {2}$$

Solution

$$\log28$$
$$=\log(14\times2)$$
$$=\log14+\log2$$ [Using: $$\log a+\log b =\log(a \times b)$$]
Hence, C is the correct option.
Question 2
1 / -0

$$\log {10}$$ is same as______

A
$$\log {6} + \log {3}$$

B
$$\log {15} + \log {3}$$

C
$$\log {21} - \log {3}$$

D
$$\log {5} + \log {2}$$

Solution

$$\log10$$
$$=\log(5\times2)$$
$$=\log5+\log2$$ [Using: $$\log a+\log b =\log(a \times b)$$]
Hence, D is the correct option.
Question 3
1 / -0

Find the characteristic of $$\log 27.93$$

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

From log table,
$$\log27.93=1.4460$$
Here, Characteristics$$=1$$ and Mantisa$$=0.4460$$
Hence, B is the correct option.
Question 4
1 / -0

Find the characteristic of $$\log 277.9301$$

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

From logarithmic table,
$$\log 277.9301=2.4439$$
Here, Characteristics$$=2$$
Hence, C is the correct option.
Question 5
1 / -0

The value of $$10^{\log_{10}{10}^{7}}$$ is:

A
$$7$$

B
$$10^7$$

C
$$10$$

D
$$\log_{10}7$$

Solution

Consider, $$10^{\log_{10}{10}^{7}} $$
$$= 10^{{{7\log}_{10}}{10}}$$
$$ = 10^{7\times 1}$$
$$ = 10^{7} $$.
Question 6
1 / -0

Find the value :
i) $$\left(\dfrac{4}{5}\right)^3 \div \left(\dfrac{4}{5}\right)^2$$
ii) $$4^7 \div 4^5$$

A
i) $$\left(\dfrac{4}{5}\right)$$
ii) $$4$$

B
i)  $$\left(\dfrac{4}{5}\right)$$
ii) $$49$$

C
i)  $$\left(\dfrac{4}{5}\right)$$
ii) $$7$$

D
i)  $$\left(\dfrac{4}{5}\right)$$
ii) $$16$$

Solution

(1)

$$\left ( \frac{4}{5} \right )^{3}\div \left ( \frac{4}{5} \right )^{2}$$

$$=\left ( \frac{4}{5} \right )^{3}\times \left ( \frac{5}{4} \right )^{2}$$

$$=\frac{4^{3}}{5^{3}}\times \frac{5^{2}}{4^{2}}$$

$$=\frac{4^{3}}{4^{2}}\times \frac{5^{2}}{5^{3}}$$

Now apply law of exponents, $$\frac{x^{m}}{x^{n}}=x^{m-n}$$

So, the expression is

$$=4^{3-2}\times 5^{2-3}$$

$$=4^{1}\times 5^{-1}$$

$$=\frac{4}{5}$$

(2)

$$4^{7}\div 4^{5}$$

$$=4^{7}\times \frac{1}{4^{5}}$$

$$=\frac{4^{7}}{4^{5}}$$

Now apply law of exponents, $$\frac{x^{m}}{x^{n}}=x^{m-n}$$

So, the expression is
$$=4^{7-5}$$
$$=4^{2}$$
$$=16$$
Question 7
1 / -0

Let $$\log_{\sqrt{8}}b=3\dfrac{1}{3},$$ then find the value of $$b$$ is

A
$$8$$

B
$$16$$

C
$$32$$

D
none of these

Solution

Given,
$$\log_{\sqrt{8}}b=3\dfrac{1}{3}$$
$$\implies b=(\sqrt{8})^{\large{\frac{10}{3}}}$$
$$\implies b=({2^3})^{\tfrac12\times\large{\frac{10}{3}}}$$
$$\implies b=2^5$$
$$\implies b=32$$.
Question 8
1 / -0

$$\log_ee^5$$ is equal to-

A
$$2.5$$

B
$$1.5$$

C
$$2$$

D
$$5$$

Solution

$$\log_ee^5=5\log_ee=5*1=5$$
Question 9
1 / -0

$$y = log \,x$$ is a solution of

A
$$xy_2 = y_1$$

B
$$xy_1 + y_2 = 0$$

C
$$xy_2 + y_1 = 0$$

D
$$xy_2 + y = 0$$

Solution

$$y=log x$$
$$y_1=\dfrac{1}{x}$$
$$xy_1=1$$
$$xy_2+y_1=0$$
$$\therefore$$ $$y=log x$$ is a solution of $$xy_2+y_1=0$$.
Question 10
1 / -0

The value of $$(0.125)^{\frac {2}{3}}$$ is

A
$$2.5$$

B
$$0.25$$

C
$$0.025$$

D
$$0.0025$$

Solution

$$ (0.125)^{\frac{2}{3}}$$

$$0.125$$ could be written as $$(0.5)^3$$

So given expression becomes'
$$\Rightarrow (0.5^3)^{\frac{2}{3}}$$

$$= (0.5)^2$$

$$= 0.25$$

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Logarithm and Antilogarithm Test 10

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Logarithm and Antilogarithm Test 10

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SHARING IS CARING

Question 1

$$\log {16} +\log {12}$$

$$\log {15} + \log {13}$$

$$\log {2} + \log {14}$$

$$\log {26} + \log {2}$$

Solution

Question 2

$$\log {6} + \log {3}$$

$$\log {15} + \log {3}$$

$$\log {21} - \log {3}$$

$$\log {5} + \log {2}$$

Solution

Question 3

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 4

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 5

$$7$$

$$10^7$$

$$10$$

$$\log_{10}7$$

Solution

Question 6

i) $$\left(\dfrac{4}{5}\right)$$ii) $$4$$

i) $$\left(\dfrac{4}{5}\right)$$ii) $$49$$

i) $$\left(\dfrac{4}{5}\right)$$ ii) $$7$$

i) $$\left(\dfrac{4}{5}\right)$$ ii) $$16$$

Solution

Question 7

$$8$$

$$16$$

$$32$$

none of these

Solution

Question 8

$$2.5$$

$$1.5$$

$$2$$

$$5$$

Solution

Question 9

$$xy_2 = y_1$$

$$xy_1 + y_2 = 0$$

$$xy_2 + y_1 = 0$$

$$xy_2 + y = 0$$

Solution

Question 10

$$2.5$$

$$0.25$$

$$0.025$$

$$0.0025$$

Solution

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i) $$\left(\dfrac{4}{5}\right)$$
ii) $$4$$

i) $$\left(\dfrac{4}{5}\right)$$
ii) $$49$$

i) $$\left(\dfrac{4}{5}\right)$$
ii) $$7$$

i) $$\left(\dfrac{4}{5}\right)$$
ii) $$16$$