Worksheet: Evaluating Logarithms with Different Bases

In this worksheet, we will practice expressing an exponential equation in logarithmic form, and vice versa, and how to evaluate logarithms with various bases.

Q1:

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

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

Q2:

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

  • A1
  • B 1 2
  • C8
  • D2
  • E4

Q3:

Find l o g 7 2 9 .

Q4:

If 3 = 2 4 , what is the value of 𝑥 ?

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

Q5:

Find the solution set of the equation l o g 3 4 3 = 3 in .

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

Q6:

Find the solution set of the equation l o g 𝑥 = 2 in .

  • A 1 9 , 1 9
  • B 1 9
  • C 1 1 6
  • D 1 9
  • E 1 3

Q7:

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

Q8:

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

Q9:

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

Q10:

Find the values of l o g 2 7 and l o g 8 1 respectively.

  • A1 , 2
  • B3, 1
  • C1 , 1
  • D3, 2
  • E2, 2

Q11:

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

Q12:

Since 1 0 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 .

Q13:

Find the value of 4 ( 2 4 . 8 4 ) 8 ( 1 4 . 3 9 ) l o g l o g correct to 4 decimal places.

Q14:

Given that l o g 4 6 = 𝑎 and l o g 5 . 8 6 = 𝑏 , find the value of 6 . Give your answer correct to four decimal places.

Q15:

Given that 𝜃 0 , 𝜋 2 , evaluate l o g s i n l o g c s c ( 𝜃 ) + ( 𝜃 ) .

Q16:

Simplify l o g 𝑥 .

  • A2
  • B 3 2
  • C10
  • D 2 3

Q17:

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

Q18:

What is the value of l o g 1 4 2 ?

  • A 3 2
  • B 5 2
  • C5
  • D 5 2
  • E 3 2

Q19:

What is the value of l o g 0 . 1 ?

Q20:

What is the value of l o g 6 4 ?

  • A 4 3
  • B 3 4
  • C12
  • D 3 4
  • E 1

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