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} \frac{\log 512}{\log 5}}  =  {\color{Black} \frac{\log 2^{9}}{\log (\frac{10}{2})}}  ={\color{Black} \frac{9\log 2}{\log10-\log 2 }} ={\color{Black} \frac{(9\times 0.3010)}{1-0.3010 }} ={\color{Black} \frac{2.709}{0.699 }} ={\color{Black} \frac{2709}{699 }} =3.876

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44 9968
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} \Rightarrow \log (3^{3})=1.431}
3 log 3 = 1.431
log 3 = 0.477
log 9 = {\color{Black} \log (3^{2})} = 2 log 3 = (2 x 0.477) = 0.954

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14 6431
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 (2^{56})=(56\times0.30103) } =16.85768.

Its characteristics is 16.

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

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8 4326
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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7 1265
Q:

A) 0 B) 1
C) 5 D) 60
 
Answer & Explanation Answer: B) 1

Explanation:

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

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

                                  \inline \fn_jvn {\color{Black}=\log_{60}60}

                                  \inline \fn_jvn {\color{Black}=1}                      

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4 1054