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Lesson: Logarithmic Equations with Different Bases

In this lesson, we will learn how to solve logarithmic equations involving logarithms with different bases.

Sample Question Videos

03:22
03:24

Worksheet • 20 Questions • 2 Videos

Q1:

Find the solution set of l o g l o g 3 9 π‘₯ = 4 in ℝ .

  • A { 2 }
  • B { 3 }
  • C { 5 }
  • D { 4 }

Q2:

Find the solution set of l o g l o g 5 1 2 5 π‘₯ = 7 2 9 in ℝ .

  • A { 9 }
  • B { 1 4 }
  • C { 5 }
  • D { 8 1 }
  • E { 7 2 9 }

Q3:

Find the solution set of l o g l o g 2 π‘₯ π‘₯ + 9 2 = 6 in ℝ .

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

Q4:

Find the solution set of l o g l o g 4 π‘₯ π‘₯ + 2 5 4 = 1 0 in ℝ .

  • A { 1 0 2 4 }
  • B { 2 5 6 }
  • C { 5 }
  • D { 4 }

Q5:

Find the solution set of l o g l o g 2 π‘₯ π‘₯ + 2 5 2 = 1 0 in ℝ .

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

Q6:

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

  • A  1 3 √ 3 
  • B  3 √ 3 
  • C { 2 7 }
  • D  1 2 7 

Q7:

Find the solution set of ο€Ί π‘₯ + 2  ο€» π‘₯ 1 6  = 5 l o g l o g 4 4 in ℝ .

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

Q8:

Determine the solution set of the equation l o g l o g 4 4 π‘₯ βˆ’ 1 π‘₯ = 8 3 in ℝ .

  • A  6 4 , 1 √ 4  3
  • B  1 6 , 1 √ 2 
  • C { 4 , 3 }
  • D { 7 }
  • E { 6 4 , 1 6 }

Q9:

Find the solution set of l o g ( 1 0 βˆ’ 9 0 ) + π‘₯ βˆ’ 3 = 0 π‘₯ in ℝ .

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

Q10:

Find the solution set of l o g l o g 2 4 π‘₯ = ( 3 π‘₯ + 2 8 ) in ℝ .

  • A { 7 }
  • B { 6 4 }
  • C { 4 }
  • D { 1 1 }
  • E { 1 2 8 }

Q11:

Determine the solution set of the equation . Give the values correct to two decimal places, if necessary.

  • A
  • B
  • C
  • D
  • E

Q12:

Find all possible values of π‘₯ for which π‘₯ = 6 4 π‘₯ l o g 2 π‘₯ βˆ’ 1 .

  • A4 or 1 8
  • B12 or 1 1 8
  • C8 or 1 4
  • D8
  • E32

Q13:

Find the solution set of 2 + 2 = 7 2 π‘₯ 9 βˆ’ π‘₯ in ℝ .

  • A { 6 , 3 }
  • B { βˆ’ 6 , βˆ’ 3 }
  • C { 6 , βˆ’ 3 }
  • D { βˆ’ 6 , 3 }

Q14:

Solve l o g l o g 2 7 π‘₯ = 1 4 9 , where π‘₯ ∈ ℝ .

  • A 1 4
  • B βˆ’ 1 4
  • C4
  • D2
  • E βˆ’ 4

Q15:

Solve l o g l o g 9 4 π‘₯ = 6 4 , where π‘₯ ∈ ℝ .

  • A729
  • B 1 2 7
  • C 1 7 2 9
  • D81
  • E27

Q16:

Solve l o g l o g 5 6 π‘₯ = 3 6 , where π‘₯ ∈ ℝ .

  • A25
  • B 1 1 0
  • C 1 2 5
  • D5
  • E10

Q17:

Solve l o g l o g 2 π‘₯ = 1 0 0 0 , where π‘₯ ∈ ℝ .

  • A8
  • B 1 6
  • C 1 8
  • D4
  • E6

Q18:

Solve ο€Ί π‘₯  βˆ’ 6 π‘₯ + 8 = 0 l o g l o g 5 2 5 , where π‘₯ ∈ ℝ .

  • A { 2 5 , 6 2 5 }
  • B { 5 , 1 2 5 }
  • C  1 2 5 , 1 6 2 5 
  • D  1 1 0 , 1 2 0 
  • E { 1 0 , 2 0 }

Q19:

Select the expression equal to

  • A l o g l o g 𝑏 𝑏 π‘₯ 𝑦
  • B l o g l o g π‘Ž π‘Ž 𝑦 π‘₯
  • C l o g l o g π‘₯ 𝑦 𝑏 𝑏
  • D l o g l o g π‘₯ 𝑦 π‘Ž π‘Ž

Q20:

Find the solution set of 2 Γ— 8 = 2 ( π‘₯ ) π‘₯ l o g l o g 8 2 8 4 in ℝ .

  • A { 5 1 2 , 8 }
  • B  4 3 
  • C { 3 , 1 }
  • D { 2 , 8 }
  • E { 6 4 , 1 }
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