Worksheet: Evaluating Logarithms

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In this worksheet, we will practice evaluating logarithms of different bases using laws of logarithms.

Q1:

Find the value of log√256, giving your answer in its simplest form.

  • A12
  • B2
  • C4
  • D8

Q2:

What is the value of log5?

Q3:

What is the value of log8?

Q4:

What is the value of log1128?

Q5:

What is the value of log128?

Q6:

What is the value of log√32√2?

Q7:

What is the value of log√1125√5?

Q8:

Find the value of loglogloglog𝑥−𝑥.

Q9:

Given that 𝐿 and 𝑀 are the two roots of the equation 𝑥−36𝑥+128=0, determine the value of loglog𝐿+𝑀.

Q10:

Calculate 24+713loglog, giving your answer to the nearest thousandth.

Q11:

What is the value of log√243√3?

Q12:

What is the value of log64?

Q13:

What is the value of log2?

Q14:

What is the value of log256?

Q15:

What is the value of log116?

Q16:

What is the value of log1256?

Q17:

What is the value of log81?

Q18:

What is the value of log243?

Q19:

What is the value of log2?

Q20:

What is the value of log14√2?

  • A5
  • B32
  • C52
  • D−32
  • E−52

Q21:

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

Q22:

Find log729.

Q23:

What is the value of loglog32256?

  • A3
  • B23
  • C58
  • D18
  • E85

Q24:

Find the value of log22.08 correct to 4 decimal places.

Q25:

What is the value of log0.1?

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