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Multiple choice logarithm and its uses basic mathematical concepts physics

Which of the following real numbers is(are) non-positive?

  1. $log{ } _{ 0.3 }(\dfrac { \sqrt { 5 } +2 }{ \sqrt { 5 } -2 }  )$

  2. $log{ } _{ 7 }(\sqrt { 83 } -9\quad )$

  3. $log{ } _{ 7\frac { \pi }{ 12 } }(cot\frac { \pi }{ 8 } \quad )$

  4. ${ log } _{ 2 }\sqrt { 9.\sqrt [ 3 ]{ { 27 }^{ \frac { -5 }{ 3 } }.243{ }^{ \frac { -7 }{ 5 } } } } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
From given,

we have,

$\log _{0.3}\left(\dfrac{\sqrt{5}+2}{\sqrt{5}-2}\right)$

$=\log _{0.3}\left(2+\sqrt{5}\right)-\log _{0.3}\left(\sqrt{5}-2\right)$

$=-2.39811$
Multiple choice logarithm and its uses basic mathematical concepts physics

If $\log x = -2.0258$, then $x$ is equal to

  1. $0.009223$

  2. $0.009423$

  3. $0.008422$

  4. $0.008223$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\log x=-2.0258$

Characteristics$=-3$
Mantissa$=-2.0258-(-3)=0.9742$
Value of $0.9742$ from antilog table $=9419+4=9423$
Number of zeroes placed after decimal will be $2.$
Antilog $-2.0258=0.009423$
Hence, B is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

The antilog of the number $2.5463$ is

  1. $251.8$

  2. $254.8$

  3. $351.8$

  4. $354.8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number before decimal point is $2,$ so decimal point will be after $3$ digits.

Value of $0.5463$ from antilog table $=3516+2=3518$
Now place a decimal point after $3$ digits of the number from left we get, $351.8$
Antilog $2.5463=351.8$
Hence, C is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

The antilog of $ (.2817)$ will be

  1. $1.19$

  2. $0.91$

  3. $0.19$

  4. $1.91$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number before decimal point is $0,$ so decimal point will be after $1$ digits.

Value of $0.2817$ from antilog table $=1910+3=1913$
Now place a decimal point after $1$ digit of the number from left we get, $1.913$
Antilog $0.2817=1.913=1.91$
Hence, D is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

What is the value of $[\log _{10} (5\log _{10} 100)]^{2}$?

  1. $4$

  2. $3$

  3. $2$

  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The value of $[\log _{10}(5\log _{10} 100)]^{2}$ is
$=[\log _{10}(5\log _{10}10^2)]^2$

$=[\log _{10}(10\log _{10}10)]^2$     .....As $\log a^m=m\log a$
$=[\log _{10}(10\times 1)]^2$     ....As $\log _aa=1$
$=[\log _{10}10]^2$
$=[1]^2=1$