Logarithm Questions MCQs


logarithm Questions

Total Questions : 47

Page 1 of 3 pages
Question 1. Which of the following statements is not correct?
  1.    log10 10 = 1
  2.    log (2 + 3) = log (2 x 3)
  3.    log10 1 = 0
  4.    log (1 + 2 + 3) = log 1 + log 2 + log 3
Answer: Option B
Question 2. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
  1.    2.870
  2.    2.967
  3.    3.876
  4.    3.912
Answer: Option C
Question 3. $${{\log \sqrt 8 } \over {\log 8}}$$  is equal to:
  1.    $$\frac{1}{6}$$
  2.    $$\frac{1}{4}$$
  3.    $$\frac{1}{2}$$
  4.    $$\frac{1}{8}$$
Answer: Option C
Question 4. If log 27 = 1.431, then the value of log 9 is:
  1.    0.934
  2.    0.945
  3.    0.954
  4.    0.958
Answer: Option C
Question 5. $${\text{If}}\,{\text{log}}\frac{a}{b} + {\text{log}}\frac{b}{a} = {\text{log}}(a + b),$$      then:
  1.    a + b = 1
  2.    a - b = 1
  3.    a = b
  4.    a2 - b2 = 1
Answer: Option A
Question 6. If $${\log _{10}}7 = a,$$   then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$   is equal to
  1.    - (1 + a)
  2.    (1 + a)-1
  3.    $$\frac{a}{10}$$
  4.    $$\frac{1}{10a}$$
Answer: Option A
Question 7. If log10 2 = 0.3010, then log2 10 is equal to:
  1.    $$\frac{{699}}{{301}}$$
  2.    $$\frac{{1000}}{{301}}$$
  3.    0.3010
  4.    0.6990
Answer: Option B
Question 8. If log10 2 = 0.3010, the value of log10 80 is:
  1.    1.6020
  2.    1.9030
  3.    3.9030
  4.    None of these
Answer: Option B
Question 9. If $${\log _{10}}5 + {\log _{10}}\left( {5x + 1} \right)$$     = $${\log _{10}}$$ $$\left( {x + 5} \right)$$ $$\, + $$ $$1,$$ then x is equal to :
  1.    1
  2.    3
  3.    5
  4.    10
Answer: Option B
Question 10. The value of $${\frac{1}{{{{\log }_3}60}} + }$$  $${\frac{1}{{{{\log }_4}60}} + }$$  $${\frac{1}{{{{\log }_5}60}}}$$   is :
Answer: Option B
Question 11. If log 2 = 0.30103, the number of digits in 264 is:
  1.    18
  2.    19
  3.    20
  4.    21
Answer: Option C
Question 12. If $${\log _x}\left( {\frac{9}{{16}}} \right) = - \frac{1}{2},$$    then x is equal to:
  1.    $$ - \frac{3}{4}$$
  2.    $$\frac{3}{4}$$
  3.    $$\frac{{81}}{{256}}$$
  4.    $$\frac{{256}}{{81}}$$
Answer: Option D
Question 13. If ax = by, then:
  1.    $$\log \frac{a}{b} = \frac{x}{y}$$
  2.    $$\frac{{\log a}}{{\log b}} = \frac{x}{y}$$
  3.    $$\frac{{\log a}}{{\log b}} = \frac{y}{x}$$
  4.    None of these
Answer: Option C
Question 14. If logx y = 100 and log2 x = 10, then the value of y is:
  1.    210
  2.    2100
  3.    21000
  4.    210000
Answer: Option C
Question 15. The value of log2 16 is:
  1.    $$\frac{1}{8}$$
  2.    4
  3.    8
  4.    16
Answer: Option B
Question 16. The value of $${\log _5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}}$$    is equal to -
  1.    725
  2.    5
  3.    3125
  4.    6
Answer: Option B
Question 17. Determine the value of $${\text{lo}}{{\text{g}}_{3\sqrt 2 }}\left( {\frac{1}{{18}}} \right)$$   is = ?
  1.    2
  2.    -2
  3.    $$\sqrt 2 $$
  4.    $$\sqrt 3 $$
Answer: Option B
Question 18. The value of $${\text{lo}}{{\text{g}}_{10}}\left( {0.0001} \right)$$   is = ?
  1.    $$\frac{1}{4}$$
  2.    $$ - \frac{1}{4}$$
  3.    $$ - 4$$
  4.    $$4$$
Answer: Option C
Question 19. What is the value of $${\left[ {{\text{lo}}{{\text{g}}_{10}}\left( {{\text{5lo}}{{\text{g}}_{10}}100} \right)\,} \right]^2}$$     = ?
  1.    1
  2.    2
  3.    10
  4.    25
Answer: Option A
Question 20. If $${\text{lo}}{{\text{g}}_8}{\text{p}} = 25$$   and $${\text{lo}}{{\text{g}}_2}{\text{q}} = 5,$$   then -
  1.    p = q15
  2.    p2 = q3
  3.    p = q5
  4.    p3 = q
Answer: Option A