Lesson Worksheet: Laws of Logarithms Mathematics

In this worksheet, we will practice using the laws of logarithms to simplify logarithmic expressions.

Q1:

Find the value of logloglog1,280−22−5 without using a calculator.

Q2:

Simplify loglog16×243.

Q3:

Determine the value of (3)−93−100loglogloglog without using a calculator.

  • Alog3
  • B23log
  • C3
  • D13log
  • Elog32

Q4:

Without using a calculator, find the approximate value of log5243 given that log5≈1.465.

Q5:

Find the approximate value of log20, given that log5≈1.161.

Q6:

Given that log3≈0.5646, find, without using a calculator, the value of log147 correct to four decimal places.

Q7:

Determine the value of logloglog7100−5623+2523 without using a calculator.

Q8:

Find the value of logloglogloglog132+142+16−12−64 without using a calculator.

Q9:

Find the value of 5×89 correct to four decimal places.

Q10:

Find the value of logloglogloglog42+47+6√6294−7√6 without using a calculator.

Q11:

Find the value of loglogloglog512×729×256×27, giving your answer in its simplest form.

Q12:

Given that log2=𝑥 and log9=𝑦, find log72 in terms of 𝑥 and 𝑦.

  • A27𝑥
  • B4𝑥+𝑦
  • C3𝑥+𝑦
  • D𝑥+3𝑦
  • E8𝑦

Q13:

Find the value of 225+12+18+72−80loglogloglog in its simplest form.

Q14:

Simplify 𝑒ln completely.

  • A𝑒
  • B14
  • Cln12
  • D12
  • E𝑒

Q15:

Evaluate logloglog𝑎+𝑏+𝑐.

Q16:

If 𝑥 is any real, positive number except 1, which of the following is equal to log𝑥?

  • A1
  • B𝑥
  • C𝑥
  • D𝑥

Q17:

Is it true that logloglog(𝑥+𝑦)=𝑥+𝑦?

  • ANo
  • BYes

Q18:

Is it true that log1=0?

  • ANo
  • BYes

Q19:

Is it true that log0=1?

  • ANo
  • BYes

Q20:

Find the value of logloglog10+16−5 without using a calculator.

Q21:

Which of the following is equal to 534+6logloglog?

  • Alog15
  • Blog243
  • Clog3
  • Dlog243
  • Elog15

Q22:

Determine the value of logloglog1−7 without using a calculator.

Q23:

Ethan and Elizabeth were both asked to solve the equation 2=3 by taking logarithms. Ethan used base 10 logarithms, while Elizabeth used the natural logarithm. When they compared results, what did they discover?

  • Alogloglnln(2)(3)=32
  • Blogloglnln(3)(10)=32
  • Clogloglnln(3)(2)=310
  • Dlogloglnln(3)(2)=32
  • Elogloglnln(3)(2)=23

Q24:

Find the perimeter of the figure below.

Q25:

Find the value of 59√3log without using a calculator.

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