PRACTICE QUESTIONS ON LOGARITHMS

Examination Questions on Logarithms

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Product Rule: loga XY = loga X + loga Y
Quotient Rule: loga X/Y = loga X – loga Y
Power Rule: loga Xy = yloga X
Change of base formula: logY X = logb X ÷ logb Y
loga a = 1
loga 1/X = –loga X

1. If log 10 a = p and log 10 b = q, then what is log 10 (a p b q) equal to?

  1. p 2 + q 2
  2. p 2 - q 2
  3. p 2 q 2
  4. p 2/ q 2

2. What is log 10(3/2) + log 10(4/3) + log 10(5/4) + ….. up to 8 terms equal to?

  1. 0
  2. 1
  3. log 10 5
  4. None of the above

3. What is the value of [log 10 (5 log 10 100)] 2?

  1. 4
  2. 3
  3. 2
  4. 1

4. What is the value of 1/2 log 10 25 – 2 log 10 3 + log 10 18?

  1. 2
  2. 3
  3. 1
  4. 0

5. What is the value of (1/3 log 10 125 – 2 log 10 4 + log 10 32 + log 10 1)?

  1. 0
  2. 1/3
  3. 1
  4. 2/5

6. What are the roots of the equation log 10(x 2 – 6x + 45) = 2 ?

  1. 9, – 5
  2. – 9, 5
  3. 11, – 5
  4. – 11, 5

7. What is the value of log 13 (10)/ log 169 (10)?

  1. 1/2
  2. 2
  3. 1
  4. log 10 13


8. If log r6 = m and log r3 = n, then what is log r( r/2) equal to?

  1. m – n + 1
  2. m + n – 1
  3. 1 – m – n
  4. 1 – m + n

9. What is the value of 2 log ( 5/8) + log( 128/125) + log( 5/2)?

  1. 0
  2. 1
  3. 2
  4. 5

10. What is log (tan 1°) + log (tan 2°) + log (tan 3°) + … + log (tan 89°) equal to?

  1. 0
  2. 1
  3. 2
  4. -1

11. What is the value of log 100 0.1?

  1. 1/2
  2. – 1/2
  3. – 2
  4. 2

12. If y = (a x) (a x)), then which one of the following is correct?

  1. log y = xylog a
  2. log y = x + ylog a
  3. log y = y + xlog a
  4. log y = (y + x) log a


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