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Worksheet: Introduction to Logarithms

Q1:

Express 2 = 2 5 6 8 in its equivalent logarithmic form.

  • A l o g 2 5 6 = 1 6
  • B l o g 8 2 5 6 = 2
  • C l o g 2 5 6 2 = 8
  • D l o g 2 2 5 6 = 8

Q2:

Express 1 0 = 1 0 0 2 in its equivalent logarithmic form.

  • A l o g 1 0 0 = 2 0
  • B l o g 2 1 0 0 = 1 0
  • C l o g 1 0 0 1 0 = 2
  • D l o g 1 0 0 = 2

Q3:

Express 2 = 1 2 8 7 in its equivalent logarithmic form.

  • A l o g 1 2 8 = 1 4
  • B l o g 7 1 2 8 = 2
  • C l o g 1 2 8 2 = 7
  • D l o g 2 1 2 8 = 7

Q4:

Find the value of the number shown with the dot on the given logarithmic scale. Round your answer to the nearest thousandth.

Q5:

What is the value of l o g l o g 2 2 6 4 8 ?

  • A1
  • B 1 2
  • C8
  • D2
  • E4

Q6:

What is the value of l o g l o g 3 3 3 2 2 5 6 ?

  • A3
  • B 8 5
  • C 1 8
  • D 5 8
  • E 2 3

Q7:

Find the value of l o g 4 2 2 . 0 8 correct to 4 decimal places.

Q8:

Use a calculator to find the number of digits of the number 3 8 7 .

Q9:

Triangle 𝐴 𝐡 𝐢 is right-angled at 𝐴 . Find its area, given that 𝐴 𝐡 = 4 9 l o g c m 2 and 𝐴 𝐢 = 5 1 2 l o g c m 7 .

Q10:

Find the values of l o g 1 4 1 9 6 and l o g 8 6 4 respectively.

  • A1, 2
  • B2, 1
  • C1, 1
  • D2, 2

Q11:

Use a calculator to find the value of l o g 5 3 . Give your answer correct to four decimal places.

Q12:

Given that l o g 4 5 4 6 = π‘Ž and l o g 5 . 8 6 = 𝑏 , find the value of 6 π‘Ž 𝑏 + 1 . Give your answer correct to four decimal places.

Q13:

Find the solution set of the equation l o g 3 π‘₯ = βˆ’ 2 in ℝ .

  • A  1 9 , βˆ’ 1 9 
  • B  βˆ’ 1 9 
  • C  1 1 6 
  • D  1 9 
  • E  1 3 

Q14:

Simplify l o g π‘₯ 4 6 √ π‘₯ .

  • A2
  • B 3 2
  • C10
  • D 2 3

Q15:

Find the solution set of the equation l o g π‘₯ 3 4 3 = 3 in ℝ .

  • A { βˆ’ 7 }
  • B { 7 , βˆ’ 7 }
  • C { 7 , 3 }
  • D { 7 }

Q16:

Since √ 1 0 β‰ˆ 3 . 1 6 , what can we conclude about l o g ( 3 ) ?

  • A l o g 3 is less than 2.
  • B l o g 3 is more than 1 2 .
  • C l o g 3 is more than 1.
  • D l o g 3 is less than 1 2 .
  • E l o g 3 is less than 1 4 .

Q17:

If 3 = 2 4 π‘₯ , what is the value of π‘₯ ?

  • A8
  • B l o g 2 4 3
  • C l o g 8
  • D l o g 3 2 4
  • E l o g 7 2

Q18:

If 6 = 5 π‘₯ , what is the value of π‘₯ ?

  • A 5 6
  • B l o g 5 6
  • C l o g 5 6
  • D l o g 6 5
  • E l o g 3 0

Q19:

Given that , evaluate .

Q20:

Find the value of 7 ( 1 5 . 6 2 ) βˆ’ 8 ( 2 0 . 9 5 ) l o g l o g 9 correct to 4 decimal places.