# Logarithms Questions

Q:

If log 2 = 0.3010 and log 3 = 0.4771, the values of log5 512 is

 A) 2.875 B) 3.875 C) 4.875 D) 5.875

Answer & Explanation Answer: B) 3.875

Explanation:

ANS:      log5512 = ${\color{Black}&space;\frac{\log&space;512}{\log&space;5}}$  =  ${\color{Black}&space;\frac{\log&space;2^{9}}{\log&space;(\frac{10}{2})}}$  =${\color{Black}&space;\frac{9\log&space;2}{\log10-\log&space;2&space;}}$ =${\color{Black}&space;\frac{(9\times&space;0.3010)}{1-0.3010&space;}}$ =${\color{Black}&space;\frac{2.709}{0.699&space;}}$ =${\color{Black}&space;\frac{2709}{699&space;}}$ =3.876

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54 15990
Q:

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

 A) 0.754 B) 0.854 C) 0.954 D) 0.654

Answer & Explanation Answer: C) 0.954

Explanation:

log 27 = 1.431
${\color{Black}&space;\Rightarrow&space;\log&space;(3^{3})=1.431}$
3 log 3 = 1.431
log 3 = 0.477
log 9 = ${\color{Black}&space;\log&space;(3^{2})}$ = 2 log 3 = (2 x 0.477) = 0.954

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20 14946
Q:

If log 2 = 0.30103, Find the number of digits in 256 is

 A) 17 B) 19 C) 23 D) 25

Answer & Explanation Answer: A) 17

Explanation:

${\color{Black}\log&space;(2^{56})=(56\times0.30103)&space;}$ =16.85768.

Its characteristics is 16.

Hence, the number of digits in ${\color{Black}2^{56}&space;}$ is 17.

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18 7859
Q:

What is the characteristic of the logarithm of 0.0000134?

 A) 5 B) -5 C) 6 D) -6

Answer & Explanation Answer: B) -5

Explanation:

log (0.0000134). Since there are four zeros between the decimal point and
the first significant digit, the characteristic is –5.

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9 1786
Q:

$\inline \fn_jvn {\color{Black}The \; value\; of\left ( \frac{1}{\log_{3}60}+ \frac{1}{\log_{4}60}+\frac{1}{\log_{5}60}\right )is:}$

 A) 0 B) 1 C) 5 D) 60

Answer & Explanation Answer: B) 1

Explanation:

$\inline&space;\fn_jvn&space;{\color{Black}Given&space;\;&space;expression=\log_{60}3+\log_{60}4+\log_{60}5}$

$\inline&space;\fn_jvn&space;{\color{Black}=\log_{60}\left&space;(&space;3\times&space;4\times&space;5&space;\right&space;)}$

$\inline&space;\fn_jvn&space;{\color{Black}=\log_{60}60}$

$\inline&space;\fn_jvn&space;{\color{Black}=1}$

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