Tag: physics

Questions Related to physics

The value of $\log _{10}0.01$ is equal to 

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $0$

  2. $-2$

  3. $-1$

  4. $4$

Show answer
Correct Option: B
Explanation:

$\log _{ 10 }{ 0.01= } \log _{ 10 }{ { 10 }^{ -2 } } $

$\log _{ 10 }{ 0.01= } -2$
Answer (B) -2

The exponential form of $\log _{10}1 = 0$ is $10^{m} = 1$,  then the value of $m$ is 

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $2$

  2. $0$

  3. $1$

  4. $6$

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Correct Option: B
Explanation:

$ \log _{ 10 }{ 1 }= 0\ 1 = { 10 }^{ 0 }$

The value of $\log _5\ 125$ is equal to

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: D
Explanation:

$ \log _{ 5 }{ 125 } =x\ 125 = { 5 }^{ x }\ x = 3 $

The value of $\log _5 1$ is equal to

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $1$

  2. $0$

  3. $7$

  4. $2$

Show answer
Correct Option: B
Explanation:

$ \log _{ 5 }{ 1 } =x\ 1\quad =\quad { 5 }^{ x }\ x\quad =\quad 0\ \ $

If exponential form of $\log _{10} 0.01 = -2$ is $10^{m} = 0.01$, then value of $m$ is equal to

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $-1$

  2. $3$

  3. $-2$

  4. $4$

Show answer
Correct Option: C
Explanation:

$ \log _{ 10 }{ 0.01 } = -2 \Rightarrow 0.01 = { 10 }^{ -2 } $

$\therefore m=-2$

Express the following in logarithmic form$\,\colon$
$81\,=\,3^{4}$

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $\log _381\,=\,4$

  2. $\log _981\,=\,2$

  3. $2\log _39\,=\,4$

  4. $4\log _93\,=\,2$

Show answer
Correct Option: A,B,C,D
Explanation:

$y={ a }^{ x }\Rightarrow \log _{ a }{ y } =x\ \therefore 81={ 3 }^{ 4 }\Rightarrow \log _{ 3 }{ 81 } =4$

A is true.
$81=3^{4}=9^{2}$

$\Rightarrow \log _{9}81=\log _{9}9^{2}=2\log _{9} 9=2$
B is true.
$81=3^{4}=9^{2}$
$\Rightarrow \log _{3} 3^{4}=\log _{3}9^{2}=2\log _{3} 9$
C is true.
$81=3^{4}=9^{2}$
$\Rightarrow \log _{9}3^{4}=\log _{9}9^{2}=2\log _{9} 9=2$
$\Rightarrow 4\log _{9} 3=2$
D is true.

If $log 27 = 1.431$, then the value of $log 9$ is

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. 0.934

  2. 0.945

  3. 0.954

  4. 0.958

Show answer
Correct Option: C
Explanation:

$log 27 = 1.431$
$\Rightarrow log (3^3) = 1.431$
$\Rightarrow 3 log 3 = 1.431$
$\Rightarrow log 3 = 0.477$
$\therefore log 9 = log (3^2) = 2 log 3 = (2 \times 0.477) = 0.954$

Find the correct expression, if $\log _{ c }{ a } =x$.

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. ${ a }^{ c }=x$

  2. ${ a }^{ x }=c$

  3. ${ c }^{ a }=x$

  4. ${ c }^{ x }=a$

  5. ${ x }^{ c }=a$

Show answer
Correct Option: D
Explanation:

Given, $\log _c a=x$

We know the change of base formula:
$\log _c a = x$  is $c^x = a$

Which of the following statements is not correct?

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. $log _{10} 10 = 1$

  2. $log (2+ 3) = log (2 \times 3)$

  3. $log _{10} 1 = 0$

  4. $log (1 + 2 + 3) = log 1 + log 2 + log 3$

Show answer
Correct Option: B
Explanation:

(a) Since $log _a a = 1,$ so $log _{10}  10 = 1$
(b) $log (2 + 3) log 5$ and $log (2 \times 3) = log 6 = log 2 + log 3$
$\therefore log(2 + 3) \neq log (2 \times 3)$
(c) Since, $log _a  1 = 0$, so, $log _{10} 1 = 0$.
(d) $log(1 + 2 + 3) = log 6 = log (1 \times 2 \times 3) = log 1 + log 2 + log 3$

If $log _{10} 2 = 0.3010$, the value of $log _{10}$ 80 is

physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

  1. 1.6020

  2. 1.9030

  3. 3.9030

  4. None of these

Show answer
Correct Option: B
Explanation:

$log _{10} 80 = log _{10} (8 \times 10)$
$= log _{10} 8 + log _{10} 10$
$=log _{10} (2^3) + 1$
$= 3 log _{10} 2 + 1$
$= (3 \times 0.3010) + 1$
$= 1.9030$