Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Logarithmic Equations

Q1:

Find π‘₯ such that l o g ( 4 π‘₯ βˆ’ 4 ) = 2 for π‘₯ .

  • A βˆ’ 2 4
  • B24
  • C βˆ’ 2 6
  • D26

Q2:

Find π‘₯ such that l o g ( βˆ’ π‘₯ + 1 ) = 1 for π‘₯ .

  • A11
  • B βˆ’ 1 1
  • C9
  • D βˆ’ 9

Q3:

Determine the solution set of the equation l o g l o g l o g 8 8 8 ( π‘₯ βˆ’ 6 ) + ( π‘₯ + 6 ) = 6 4 in ℝ .

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

Q4:

Determine the solution set of the equation l o g l o g l o g 4 4 4 ( π‘₯ βˆ’ 3 ) + ( π‘₯ + 3 ) = 1 6 in ℝ .

  • A { 2 }
  • B { 5 , βˆ’ 5 }
  • C { 2 , βˆ’ 2 }
  • D { 5 }
  • E { 4 }

Q5:

Find the solution set of l o g l o g 6 6 ( βˆ’ 2 π‘₯ + 4 8 ) = 2 π‘₯ in ℝ .

  • A { 5 }
  • B { 8 }
  • C { 1 4 }
  • D { 6 }
  • E { 7 }

Q6:

Find the solution set of l o g l o g l o g 6 2 6 6 ο€Ή 9 π‘₯ βˆ’ 2 7  = 2 π‘₯ + 1 3 2 1 6 in ℝ .

  • A { 4 }
  • B { 9 }
  • C  3 3 8 
  • D { 3 }
  • E { 6 }

Q7:

Find the solution set of l o g l o g l o g l o g π‘₯ π‘₯ π‘₯ π‘₯ 5 + 4 0 βˆ’ 2 4 = 2 + 8 in ℝ .

  • A { 2 }
  • B  4 5 
  • C  1 4 
  • D  5 4 

Q8:

Determine the solution set of the equation 2 Γ— 5 = 6 4 0 0 0 3 π‘₯ π‘₯ l o g l o g 3 3 in ℝ .

  • A { 4 0 }
  • B { 3 }
  • C { 8 }
  • D { 2 7 }

Q9:

Find the solution set of l o g l o g π‘₯ 2 Γ— 2 π‘₯ = βˆ’ 4 in ℝ .

  • A  2 0 , 1 5 0 
  • B  1 0 0 , 1 1 0 0 
  • C { 2 0 0 , 1 0 0 }
  • D  2 0 0 , 1 5 0 
  • E { 2 0 , 1 0 }

Q10:

Determine 𝑓 ( 2 4 3 ) , given that the graph of the function 𝑓 ( π‘₯ ) = π‘₯ l o g π‘Ž passes through the point ( 8 1 , 4 ) .

Q11:

Solve l o g l o g 2 3 2 ο€Ί ο€Ή π‘₯ βˆ’ 8 π‘₯   = 1 , where π‘₯ ∈ ℝ .

  • A { βˆ’ 2 , 2 7 }
  • B { βˆ’ 9 , 1 }
  • C { βˆ’ 8 , 8 }
  • D { βˆ’ 1 , 9 }
  • E { 2 , 3 }

Q12:

Find the solution set of l o g l o g l o g l o g 9 9 9 9 6 2 1 6 Γ— 8 1 = 3 6 Γ— π‘₯ in ℝ .

  • A { 2 7 }
  • B { 9 }
  • C { 2 }
  • D { 3 }
  • E { 8 1 }

Q13:

Solve 5 = 1 5 l o g 6 π‘₯ , where π‘₯ ∈ ℝ .

  • A 6 5
  • B6
  • C1
  • D 1 6

Q14:

Solve l o g 2 π‘₯ ( 2 + 5 1 0 ) = 1 0 βˆ’ π‘₯ , where π‘₯ ∈ ℝ .

Q15:

Determine the solution set of the equation l o g l o g 3 2 3 ο€Ή π‘₯ βˆ’ 5 π‘₯ + 4  = 4 + ( π‘₯ βˆ’ 1 ) in ℝ .

  • A { 4 }
  • B { 7 7 }
  • C { 1 }
  • D { 8 5 }

Q16:

Find the solution set of 3 + 2 4 3 = 2 4 4 Γ— 3 2 π‘₯ π‘₯ in ℝ .

  • A { 5 }
  • B { 0 , βˆ’ 5 }
  • C { βˆ’ 5 , 5 }
  • D { 0 , 5 }

Q17:

Find the solution set of 4 + 2 = 5 1 6 π‘₯ π‘₯ + 8 in ℝ .

  • A { 2 }
  • B { βˆ’ 1 }
  • C { 3 }
  • D { 1 }

Q18:

Find the solution set of ο€Ί π‘₯  + π‘₯ + 1 = ο€Ί 2  l o g l o g l o g 7 2 7 2 7 2 in ℝ .

  • A { 4 9 , 1 4 }
  • B  7 2 , 1 4 
  • C { 1 4 , βˆ’ 1 4 }
  • D  2 7 , 1 1 4 
  • E  2 7 , 7 

Q19:

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

  • A { βˆ’ 1 }
  • B { 8 }
  • C { 1 0 }
  • D { 2 }
  • E { 6 }

Q20:

Find the solution set of 3 + 2 4 3 3 = 3 6 π‘₯ π‘₯ in ℝ .

  • A { βˆ’ 3 , 2 }
  • B { βˆ’ 3 , βˆ’ 2 }
  • C { 3 , βˆ’ 2 }
  • D { 3 , 2 }

Q21:

Solve l o g 4 2 π‘₯ βˆ’ 2 6 π‘₯ βˆ’ 7 π‘₯ + 6 = 1 , where π‘₯ ∈ ℝ .

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

Q22:

Solve l o g 4 2 π‘₯ βˆ’ 6 π‘₯ π‘₯ βˆ’ 4 = 1 , where π‘₯ ∈ ℝ .

  • A { 2 , 4 }
  • B { βˆ’ 2 , βˆ’ 8 }
  • C { 2 }
  • D { 2 , 8 }
  • E { 1 , 8 }

Q23:

What is the solution set of the equation l o g π‘₯ ( 9 π‘₯ βˆ’ 1 8 ) = 2 ?

  • A { 2 }
  • B  2 0 9 
  • C βˆ…
  • D { 3 , 6 }

Q24:

Find the solution set of 4 βˆ’ 1 0 2 6 Γ— 2 + 2 0 4 8 = 0 π‘₯ + 8 π‘₯ + 8 2 2 in ℝ .

  • A { 2 , βˆ’ 2 , 7 , βˆ’ 7 }
  • B { 2 , βˆ’ 2 }
  • C { 2 , βˆ’ 7 }
  • D  √ 2 , βˆ’ √ 2 

Q25:

Solve the equation l o g ο€Ή π‘₯ βˆ’ π‘₯ βˆ’ 2  = 1 2 , where π‘₯ ∈ ℝ .

  • A { 1 2 , βˆ’ 1 2 }
  • B { 3 , βˆ’ 4 }
  • C { βˆ’ 1 , 2 }
  • D { βˆ’ 3 , 4 }
  • E { 1 , βˆ’ 2 }