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Lesson: Properties of Logarithms

Sample Question Videos

Worksheet • 22 Questions • 1 Video

Q1:

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

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

Q2:

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 βˆ’ 1 π‘₯ + 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 π‘₯ Γ· 𝑦

Q3:

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

Q4:

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.

Q5:

Find the value of l o g l o g l o g l o g 6 6 6 6 4 + 2 7 Γ— 8 1 7 2 9 without using a calculator.

Q6:

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

  • Ayes
  • Bno

Q7:

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‘₯ + 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‘₯ βˆ’ 𝑦

Q8:

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

Q9:

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

Q10:

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

Q11:

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

  • A 2 3
  • B5
  • C2
  • D 3 2
  • E9

Q12:

Find the perimeter of the figure below.

Q13:

Determine the perimeter of the figure below.

Q14:

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

  • A 1 2
  • B5
  • C4
  • D2
  • E12

Q15:

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

Q16:

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 .

Q17:

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

Q18:

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

Q19:

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

Q20:

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

Q21:

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

Q22:

Find the solution set of l o g l o g l o g l o g 9 9 2 9 9 2 7 2 9 π‘₯ = ο€Ί 2  βˆ’ 8 ο€»  in ℝ .

  • A { 2 }
  • B { 8 1 }
  • C { 3 }
  • D { 4 }
  • E { 1 }
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