Tag: physics

Quizzes (598) Questions (13441)

Questions Related to physics

Multiple choice physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

If $log _x \left( \dfrac{9}{16} \right) = - \dfrac{1}{2}$, then x is equal to

  1. $- \dfrac{3}{4}$
  2. $\dfrac{3}{4}$
  3. $\dfrac{81}{256}$
  4. $\dfrac{256}{81}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$log _x \left( \dfrac{9}{16} \right ) = - \dfrac{1}{2}$
$\Rightarrow x^{-1/2} = \dfrac{9}{16}$
$\Rightarrow \dfrac{1}{\sqrt x} = \dfrac{9}{16}$
$\Rightarrow \sqrt x = \dfrac{16}{9}$
$\Rightarrow x = \left( \dfrac{16}{9} \right)^2$
$\Rightarrow x = \dfrac{256}{81}$

Multiple choice physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

What is the value of $\dfrac {1}{2}\log _{10} 25 - 2 \log _{10} 3 +\log _{10} 18$?

  1. $2$
  2. $3$
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The value of $\dfrac {1}{2}\log _{10} 25 - 2 \log _{10} 3 +\log _{10} 18$ is
$= \log _{10}(25)^{1/2} - \log _{10} (3)^{2} + \log _{10}18$
$= \log _{10}5 - \log _{10}9 + \log _{10}18$
$= \log _{10} \left (\dfrac {5}{9}\times 18\right ) $

$= \log _{10} 10 $    ....Using the identity $\log _aa=1$
$= 1$

Multiple choice physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

The logarithmic form of ${5}^{2}=25$ is

  1. $\log _{ 5 }{ 2 } =25$
  2. $\log _{ 2 }{ 5 } =25$
  3. $\log _{ 5 }{ 25 } =2$
  4. $\log _{ 25 }{ 5 } =2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$5^2=25$

Taking log with base $5$ both sides, we get
$\log _55^2=\log _525$
$\Rightarrow \log _525=2\log _55$
$\Rightarrow \log _525=2$     $(\log _aa=1)$
Hence, C is the correct option.

Multiple choice physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

If mantissa of logarithm of 719.3 to the base 10 is 0.8569 , then mantissa of logarithm  of 71.93 is

  1. 0.8569
  2. $\overline 1 .8569$

  3. 1.8569

  4. 0.1431
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mantissa of logarithm of $719.3$ to base $10$ is $0.8569$

Then, mantissa of logarithm of $71.93$ is also $0.8569$
As, $\log _{10}{(719.3)}=2+(0.8569)$(mantissa)
So, $\log _{10}{(71.93)}=1+(0.8596)$ (mantissa)

Multiple choice physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

If $2\log y -\log x -3=0$, express $x$ in terms of $y.$

  1. $x=\dfrac{y^2}{e^3}$
  2. $x=\dfrac{y^2}{e^2}$
  3. $x^2=\dfrac{y^2}{e^3}$
  4. $x=\dfrac{y^3}{e^3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\Rightarrow$$\log { { y }^{ 2 } } -\log { x } -\log { { e }^{ 3 } } =0$.......$\log e=1$

$\Rightarrow$$ \log { x } =\log { \left (\cfrac { { y }^{ 2 } }{ { e }^{ 3 } } \right ) } $

$\Rightarrow$$ x=\cfrac { { y }^{ 2 } }{ { e }^{ 3 } } $

Multiple choice physics logarithms introduction to logarithm logarithmic notation exponential and logarithms

If $2\log y -\log x-3=0$ express $x$ in terms of $y.$

  1. $x^2=1000y$
  2. $x^2= \dfrac{y^2}{e^3}$
  3. $y^2= \dfrac{x}{1000}$
  4. $y^2= 1000x$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given: $2\log y -\log x-3=0$

$\log { { y }^{ 2 } } -\log { x } -3\log { { e }=0 } $.......$(\log e=1)$

$\log { { y }^{ 2 } } -\log { x } -\log { { e }^{ 3 }=0 } $

$ \log { x } =\log { { y }^{ 2 } } -\log { { e }^{ 3 } } =\log { \left (\cfrac { { y }^{ 2 } }{ { e }^{ 3 } } \right ) } $

$ x=\cfrac { { y }^{ 2 } }{ { e }^{ 3 } } $