Mathematics · Quantitative Aptitude

Logarithms

246 Questions

Logarithms are mathematical operations that determine the exponent required for a base to reach a specific number. This topic tests the application of logarithmic properties, changing bases, and solving complex equations. It is a high-yield topic for quantitative aptitude in competitive exams.

Logarithmic expressionsBase change propertiesSolving log equationsInfinite series logsCharacteristic values

Logarithms Questions

Multiple choice logarithm and its uses basic mathematical concepts physics

Antilog of the number $( -8.654)$ is equal to

  1. $2.18\times 10^{-8}$
  2. $2.18\times 10^{-9}$
  3. $2.218\times 10^{-9}$
  4. $2.218\times 10^{-8}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$(-8.654)=-8+(-0.654)$
$=-8+(-0.654)+1-1$
$=-9+(1-0.654)=-9+0.346$

Actual digits of 0.346 from the log table $=2.218$

$\therefore$ $ anti \log(-8.654)=2.218\times 10^{-9}$
Multiple choice logarithm and its uses basic mathematical concepts physics

The antilog of $\overline {1}.8840$is equal to

  1. $76.56$
  2. $\overline {1}.7656$
  3. $0.7656$
  4. $7.656$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Antilog $\bar1.8840$

Characteristics$=-1$
Value of $0.8840$ from antilog table $=7656$

Now number of zeroes after decimal will be $0.$
Antilog $\bar1.8840=0.7656$
Hence, C is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

The antilog of the number $0.2015$ is equal to

  1. $\overline {1}.1591$
  2. $1.591$
  3. $0.01591$
  4. $15.91$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Value of $0.2015$ from antilog table $=1589+2+=1591$
Now place a decimal point after $1$ digits of the number from left we get, $1.591$
Antilog $0.2015=1.591$
Hence, B is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

Evaluate using log tables: $\sqrt [3] {\dfrac {16.23}{426.8}}$

  1. $0.6332$
  2. $0.3632$
  3. $0.3362$
  4. $0.3624$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\log { y } =\cfrac { 1 }{ 3 } \left[ \log { (16.23) } -\log { (426.8) }  \right] \ \log { y } =\cfrac { 1 }{ 3 } \left[ 1.2103-2.63022 \right] \ \log { y } =-0.4733\ y={ 10 }^{ -0.4733 }=0.3362$

Multiple choice logarithm and its uses basic mathematical concepts physics

If $f(x) = \log x$, then $f^{-1}x  $ is

  1. $\log\dfrac1x$
  2. $\log x^2$
  3. $anti\log(x)$
  4. $anti\log\dfrac1x$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let,$f(x)=y=\log x$

$\Rightarrow f(x)=y=\log x$
$\Rightarrow $ anti$\log (y)=x$
Therefore, Inverse of $f(x)$ i.e. $f^{-1}(x)=$anti$\log (x)$
Hence, C is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

The value of $\log _{10} 8$ is equal to

  1. $.903$
  2. $3.901$
  3. $.301$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\log _{10}8=\log _{10}2^3=3\log _{10}2$

$=3\times 0.301$   $(\log _{10}2=0.301)$
$=0.903$
Hence, D is the correct option.

Multiple choice logarithm and its uses basic mathematical concepts physics

Find the value of $\dfrac {\log _{10} 72}{\log _{10} 8}$ using log table

  1. $\log _{10} 9$
  2. $1+\dfrac{.954}{.903}$
  3. $2$
  4. $\dfrac{.903+.954}{.954}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\dfrac{\log _{10}{72}}{\log _{10}{8}}=\dfrac{\log _{10}{(8\times9)}}{\log _{10}{8}}=\dfrac{\log _{10}{8}+\log _{10}{9}}{\log _{10}{8}}$
$=1+\dfrac{\log _{10}{3^{2}}}{\log _{10}{2^{3}}}=1+\dfrac{2\log _{10}{3}}{3\log _{10}{2}}$
$=1+\dfrac{2.(0.477)}{3.(0.301)}=1+\dfrac{(0.954)}{(0.903)}$
Multiple choice logarithm and its uses basic mathematical concepts physics

Find the value of $\log _{10} 72$ using log table

  1. $0.901+0.909$
  2. $0.903+0.954$
  3. $1.890$
  4. $2.104$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\log _{10}{72}=\log _{10}(2^{3}.3^{2})$
$=\: \log _{10}{2^{3}}+\log _{10}{3^{2}}$
$=\: 3.\log _{10}{2}+2.\log _{10}{3}$
$=\: 3(0.301)+2(0.4771)$
$=\: 0.903+0.954$
Multiple choice logarithm and its uses basic mathematical concepts physics

Find the value of $\log _{10} {\dfrac{64^{2.1}\times 81^{4.2}}{49^{3.4}}}$ using log table

  1. $2.1 \times 6 \times .303+ 4.2 \times 2 \times .854- 3.4 \times 2 \times .745$
  2. $2.1 \times .303+ 4.2 \times .954- 3.4 \times .845$
  3. $2.1 \times 6 \times .303- 4.2 \times 2 \times .954+3.4 \times 2 \times .845$
  4. $2.1 \times 6 \times .303+ 4.2 \times 2 \times .954- 3.4 \times 2 \times .845$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$\log _{10}{64^{2.1}}+\log _{10}{81^{4.2}}-\log _{10}{49^{3.4}}$
$= 2.1\log _{10}{64}+4.2\log _{10}{81}-3.4\log _{10}{49}$
$=2.1\log _{10}{2^{6}}+4.2\log _{10}{3^{4}}-3.4\log _{10}{7^{2}}$
$=2.1\times6\times(0.303)+4.2\times4\times(0.477)-3.4\times2\times(0.845)$
$=2.1\times6\times(0.303)+4.2\times2\times(0.954)-3.4\times2\times(0.845)$
Multiple choice logarithm and its uses basic mathematical concepts physics

Let $x = (0.15)^{20}$. Find the characteristic in the logarithm of $x$ to the base $10$.

  1. $17$
  2. $21$
  3. $-21$
  4. $-17$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given $x=(0.15)^{20}$

By applying $\log$ on both sides , we get $\log _{ 10 }{ x } =20\log _{ 10 }{ (0.15) } =-16.478$
$\Rightarrow \log _{ 10 }{ x } =-17+0.5218$
The integral part of $\log _{ 10 }{ x } $ is called characteristic
Therefore the characteristic of given number is $-17$
So option $D$ is correct

Multiple choice logarithm and its uses basic mathematical concepts physics

Find the value of ${\log _{10} 72} + {\log _{10} {\dfrac{1}{8}}}$ using log table

  1. $0.903$
  2. $0.303$
  3. $0.954$
  4. $1.234$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\log _{10}{72}+\log _{10}\left (\dfrac{1}{8}  \right )$
$=\: \log _{10}{\left (72\times \dfrac{1}{8}  \right )}=\log _{10}{9}=\log _{10}{3^{2}}$
$=\: 2.\log _{10}{3}=2(0.477)=0.954$
Multiple choice logarithm and its uses basic mathematical concepts physics

If the mantissa of $\log 2125 =3.3275$, find the mantissa of $\log21.25$

  1. $1.3273$
  2. $2.3273$
  3. $0.3273$
  4. $32.2321$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that:

$\log2125=3.3273$
Now, $\log21.25=\log\cfrac{2125}{100}$
$=\log 2125-\log100$
$=3.3273-\log10^2$
$=3.3273-2$
$=1.3273$

Multiple choice logarithm and its uses basic mathematical concepts physics

The logarithm of $0.0625$ to the base $2$ is:

  1. $0.025$
  2. $0.25$
  3. $5$
  4. $-4$
  5. $-2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\log _{2}{\cfrac{625}{10000}}$

$=\log _{2}{\cfrac{1}{16}}$
$=\log _{2}{(16)^{-1}}$
$=\log _{2}{(2)^{-4}}$
$=-4\log _{2}{2}$
$= -4$

Multiple choice logarithm and its uses basic mathematical concepts physics

Given $log _{10}2=a$ and $log _{10}3=b$, if $3x+2=25$, the value of x in terms of $a$ and $b$ is $x=(10^{k}+1)$. K=?

  1. $\dfrac{a-1}{b}$
  2. $a-b+1$
  3. $\dfrac{1+a}{b}$
  4. $\dfrac{b}{1-a}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\log _{10}{2}=a$

$\Rightarrow 2=(10^a)$
$\log _{10}{3}=b$
$\Rightarrow 3=(10^b)$
$3x+2=25$
$x=\cfrac{23}{3}=(2\times \cfrac{10}{3}+1)=10\cfrac{(10)^a}{(10)^b}+1$
$x=10^{(a+1-b)}+1$
$x=(10^{a-b+1}+1)$