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Worksheet: The Properties of Logarithms

Q1:

If π‘₯ is any positive, real number, which of the following is equal to l o g π‘₯ 𝑛 ?

  • A l o g π‘₯
  • B 𝑛
  • C l o g π‘₯ 𝑛
  • D 𝑛 π‘₯ l o g

Q2:

Is it true that l o g l o g l o g π‘Ž π‘Ž π‘Ž ( π‘₯ + 𝑦 ) = π‘₯ Γ— 𝑦 ?

  • Ano
  • Byes

Q3:

Which of the following is equal to l o g π‘Ž ( π‘₯ 𝑦 ) ?

  • A l o g l o g π‘Ž π‘Ž π‘₯ βˆ’ 𝑦
  • B l o g l o g π‘Ž π‘Ž π‘₯ Γ— 𝑦
  • C l o g l o g π‘Ž βˆ’ 1 π‘Ž βˆ’ 1 π‘₯ + 𝑦
  • D l o g l o g π‘Ž π‘Ž π‘₯ + 𝑦

Q4:

Which of the following is equal to l o g π‘Ž ο€½ π‘₯ 𝑦  ?

  • A l o g l o g π‘Ž π‘Ž π‘₯ Γ· 𝑦
  • B l o g l o g π‘Ž π‘Ž π‘₯ Γ— 𝑦
  • C l o g l o g π‘Ž π‘Ž π‘₯ + 𝑦
  • D l o g l o g π‘Ž π‘Ž βˆ’ 1 π‘₯ + 𝑦

Q5:

Find the value of l o g l o g l o g 2 2 2 1 0 + 1 6 βˆ’ 5 without using a calculator.

Q6:

Find the value of l o g l o g l o g 3 3 3 2 8 + 4 5 βˆ’ 1 4 0 without using a calculator.

Q7:

If l o g l o g 9 9 π‘₯ + 9 = 2 , what is the value of π‘₯ ?

Q8:

If l o g l o g 3 3 π‘₯ + 1 = 4 , what is the value of π‘₯ ?

Q9:

If l o g l o g l o g 6 6 6 π‘₯ βˆ’ 7 = 1 0 , what is the value of π‘₯ ?

Q10:

Find the value of l o g l o g l o g l o g 7 7 7 7 3 2 + 8 1 0 βˆ’ 5 without using a calculator.

Q11:

Find the solution set of l o g l o g l o g 9 2 9 9 π‘₯ + 2 = 3 2 in ℝ .

  • A { 9 , βˆ’ 9 }
  • B { 8 , βˆ’ 8 }
  • C { 1 6 , βˆ’ 1 6 }
  • D { 4 , βˆ’ 4 }

Q12:

Find the solution set of l o g l o g l o g ( π‘₯ + 8 ) + ( π‘₯ βˆ’ 8 ) = ( 1 9 π‘₯ + 2 ) in ℝ .

  • A { 8 }
  • B { βˆ’ 3 }
  • C { 1 0 }
  • D { 2 2 }
  • E { 1 9 }

Q13:

Which of the following is equal to 5 3 4 + 6 l o g l o g l o g ?

  • A l o g 1 5
  • B l o g 2 4 3
  • C l o g 2 4 1 5
  • D l o g 2 4 2 4 3
  • E l o g 3

Q14:

Calculate l o g l o g l o g l o g 1 6 βˆ’ 2 5 6 4 βˆ’ 1 2 5 .

  • A9
  • B2
  • C 3 2
  • D 2 3
  • E5

Q15:

Find the perimeter of the figure below.

Q16:

Determine the perimeter of the figure below.

Q17:

Simplify l o g l o g 7 7 1 6 2 5 6 .

  • A12
  • B4
  • C2
  • D 1 2
  • E5

Q18:

Find the value of 5 9 √ 3 l o g 3 5 without using a calculator.

Q19:

Find the value of 1 8 π‘Ž + 1 8 𝑏 + 5 5 𝑐 βˆ’ √ π‘Ž 𝑏 βˆ’ 5 𝑐 l o g l o g l o g l o g l o g 5 5 5 5 5 5 8 .

Q20:

Find the solution set of l o g l o g l o g ( π‘₯ + 5 ) + ( π‘₯ βˆ’ 5 ) = 3 βˆ’ 5 in ℝ .

  • A { 6 }
  • B { 2 3 }
  • C { 2 0 0 }
  • D { 1 5 }
  • E { 5 }

Q21:

Find the solution set of l o g l o g l o g 8 2 8 6 ο€Ή π‘₯ + 5 0 π‘₯ βˆ’ 7 9  βˆ’ ( π‘₯ βˆ’ 2 ) = 3 6 in ℝ .

  • A { 6 }
  • B { 2 }
  • C { 1 0 }
  • D { 7 }

Q22:

Find the solution set of l o g l o g l o g 2 2 2 4 ο€Ή π‘₯ + 2 π‘₯ βˆ’ 7 1  βˆ’ ( π‘₯ βˆ’ 1 0 ) = 6 4 in ℝ .

  • A { 4 }
  • B { 1 0 }
  • C { 5 }
  • D { 3 }

Q23:

Find the solution set of 4 ( π‘₯ + 5 ) βˆ’ ( π‘₯ βˆ’ 3 ) = 6 2 5 l o g l o g l o g 2 2 4 2 in ℝ .

  • A { 1 1 }
  • B { 2 }
  • C { 7 }
  • D { 5 }

Q24:

Find the solution set of ο€Ί π‘₯  = π‘₯ l o g l o g 4 3 4 4 in ℝ .

  • A  1 6 , 1 4 
  • B  6 4 , 1 6 4 
  • C { 1 6 }
  • D  1 6 , 1 1 6 
  • E  4 , 1 1 6 

Q25:

Find the solution set of ο€Ί π‘₯  βˆ’ π‘₯ = 8 l o g l o g 2 2 2 βˆ’ 7 in ℝ .

  • A  2 5 6 , 1 1 2 8 
  • B  2 5 6 , 1 2 
  • C { 2 }
  • D  2 , 1 2 5 6 
  • E  1 2 8 , 1 2 5 6 