Logarithm and Antilogarithm Test 9

Result

Logarithm and Antilogarithm Test 9

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The exponential form of $$\log _{ 2 }{ 16 } =4$$ is

A
$${2}^{4}=16$$

B
$${4}^{2}=16$$

C
$${2}^{16}=4$$

D
$${4}^{16}=2$$

Solution

Since, $$\log_2 16=4$$
$$\implies \log $$ of $$16$$ to the base $$2$$ is $$4$$
$$\Rightarrow 16=2^4$$
Hence, A is the correct option.
Question 2
1 / -0

$$p^{0}$$ is equal to

A
$$0$$

B
$$1$$

C
$$-1$$

D
$$p$$

Solution

As we can see that $$p$$ is raised to power $$0$$. It means that there is no term of $$p$$.

So, $$p^{0}=1$$
Any real number when raised to the power $$0$$ gives $$1$$.
Question 3
1 / -0

If $$\log _8 m+{\log}_8\dfrac{1}{6}=\dfrac{2}{3}$$, then m is equal to

A
24

B
18

C
12

D
4

Solution

$$\log_8m+\log_8\cfrac16=\cfrac23$$
$$\Rightarrow \log_8\cfrac m6=\cfrac23$$
$$\Rightarrow \cfrac m6=8^{\cfrac23}$$
$$\Rightarrow m=6\times 2^2$$
$$\Rightarrow m=24$$
Hence, A is the correct option.
Question 4
1 / -0

Simplify the following using law of exponents.
$$2^{10}\times 2^4$$

A
$$2^{10}$$

B
$$2^{12}$$

C
$$2^{13}$$

D
$$2^{14}$$

Solution

we know that,

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

so,
$$2^{10}\times 2^4$$

$$=2^{10+4}$$

$$=2^{14}$$
Question 5
1 / -0

Find the mantissa of $$\log 2.125$$

A
$$1.3273$$

B
$$2.3273$$

C
$$0.3273$$

D
$$32.2321$$

Solution

From Logarithmic table,
$$\log2.125=0.3273$$
Here, Characteristics$$=0,$$ Mantissa$$=0.3273$$
Hence, C is the correct option.
Question 6
1 / -0

$$\log {(2\times 3\times 4)}$$ is equal to:

A
$$\log {2} + \log {3} +\log {4}$$

B
$$\log {12}$$

C
$$\log {9}$$

D
$$\log {4}$$

Solution

$$\log(2\times3\times4)$$
$$=\log2+\log3+\log4$$ $$(\log(a\times b)=\log a+\log b)$$
Hence, A is the correct option.
Question 7
1 / -0

Evaluate $$2^0+3^0$$

A
$$2$$

B
$$3$$

C
$$5$$

D
$$1$$

Solution

Question 8

1 / -0

Match the following provided that $$a$$ and $$b$$ any two rational numbers different from zero and $$x, y$$ are any two rational numbers.

$$(1)$$	$$a^{x} \times a^{y}$$	$$(a)$$	$$a^{x - y}$$
$$(2)$$	$$a^{x} \div a^{y}$$	$$(b)$$	$$a^{xy}$$
$$(3)$$	$$(a^{x})^{y}$$	$$(c)$$	$$a^{x + y}$$
$$(4)$$	$$(ab)^{x}$$	$$(d)$$	$$\dfrac {a^{x}}{b^{x}}$$
$$(5)$$	$$\left (\dfrac {a}{b}\right )^{x}$$	$$(e)$$	$$a^{x}\times b^{x}$$

$$1 - (c), 2 - (a) , 3 - (b), 4 - (e), 5 - (d)$$

$$1 - (b), 2 - (c) , 3 - (a), 4 - (e), 5 - (d)$$

$$1 - (a), 2 - (c) , 3 - (d), 4 - (e), 5 - (b)$$

$$1 - (a), 2 - (b) , 3 - (c), 4 - (d), 5 - (e)$$

Solution

(1) If base is same then the product of two exponential numbers is same as base raised to the power equal to sum of exponents of each.

$$\therefore a^{x}\times a^{y} = a^{x+y}$$

(2) If base is same then the division of two exponential numbers is same as base raised to the power equal to difference of exponents of each.

$$\therefore a^{x}\div a^{y} = a^{x-y}$$

(3) $$(a^{x})^{y} = a^{xy}$$

(4) $$(ab)^x = (a^{x}b^{x}) = a^{x}\times b^{x}$$

(5) $$(\dfrac{a}{b})^{x} = a^{x}\div b^{x} = \dfrac{a^{x}}{b^{x}}$$

Question 9
1 / -0

Find the characteristic of $$\log 7.93$$

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

From Logarithmic table,
$$\log7.93=0.89927$$
Here, Characteristics$$=0$$
Hence, A is the correct option.
Question 10
1 / -0

If $$\left(\dfrac{3}{2}\right)^2 \times \left(\dfrac{3}{2}\right)^{a+5}=\left(\dfrac{3}{2}\right)^8$$, then $$a =$$______ .

A
$$-1$$

B
$$0$$

C
$$1$$

D
$$2$$

Solution

$$\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^{a+5}=\left(\dfrac{3}{2}\right)^8\Rightarrow \left(\dfrac{3}{2}\right)^{a+7}=\left(\dfrac{3}{2}\right)^8$$
On comparing, we get, $$a+7=8 \Rightarrow a=1$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Logarithm and Antilogarithm Test 9

Result

Logarithm and Antilogarithm Test 9

Score

-

Rank

-

SHARING IS CARING

Question 1

$${2}^{4}=16$$

$${4}^{2}=16$$

$${2}^{16}=4$$

$${4}^{16}=2$$

Solution

Question 2

$$0$$

$$1$$

$$-1$$

$$p$$

Solution

Question 3

24

18

12

4

Solution

Question 4

$$2^{10}$$

$$2^{12}$$

$$2^{13}$$

$$2^{14}$$

Solution

Question 5

$$1.3273$$

$$2.3273$$

$$0.3273$$

$$32.2321$$

Solution

Question 6

$$\log {2} + \log {3} +\log {4}$$

$$\log {12}$$

$$\log {9}$$

$$\log {4}$$

Solution

Question 7

$$2$$

$$3$$

$$5$$

$$1$$

Solution

Question 8

$$1 - (c), 2 - (a) , 3 - (b), 4 - (e), 5 - (d)$$

$$1 - (b), 2 - (c) , 3 - (a), 4 - (e), 5 - (d)$$

$$1 - (a), 2 - (c) , 3 - (d), 4 - (e), 5 - (b)$$

$$1 - (a), 2 - (b) , 3 - (c), 4 - (d), 5 - (e)$$

Solution

Question 9

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 10

$$-1$$

$$0$$

$$1$$

$$2$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.