## Logarithms

Quantitative aptitude questions are asked in many competitive exams and placement exam. 'Logarithms' is a category in Quantitative Aptitude. Quantitative aptitude questions given here are extremely useful for all kind of competitive exams like Common Aptitude Test (CAT), MAT, GMAT, IBPS Exam, CSAT, CLAT, Bank Competitive Exams, ICET, UPSC Competitive Exams, CLAT, SSC Competitive Exams, SNAP Test, KPSC, XAT, GRE, Defense Competitive Exams, L.I.C/ G. I.C Competitive Exams, Railway Competitive Exam, TNPSC, University Grants Commission (UGC), Career Aptitude Test (IT Companies) and etc., Government Exams etc.

We have a large database of problems on "Logarithms" answered with explanation. These will help students who are preparing for all types of competitive examinations.

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

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

Subject: Logarithms - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

41

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

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

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

Subject: Logarithms - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

12

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

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

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.

Subject: Logarithms - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

8

What is the characteristic of the logarithm of 0.0000134?

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

Explanation:

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

Subject: Logarithms - Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams
Job Role: Bank PO

7

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

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

Explanation:

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

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

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

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