Worksheet: Logarithmic Equations with Different Bases

In this worksheet, we will practice solving logarithmic equations involving logarithms with different bases.

Q1:

Find the solution set of l o g l o g 3 9 𝑥 = 4 in .

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

Q2:

Select the expression equal to

  • A l o g l o g 𝑥 𝑦 𝑎 𝑎
  • B l o g l o g 𝑎 𝑎 𝑦 𝑥
  • C l o g l o g 𝑥 𝑦 𝑏 𝑏
  • D l o g l o g 𝑏 𝑏 𝑥 𝑦

Q3:

Find the solution set of l o g l o g 2 𝑥 𝑥 + 9 2 = 6 in .

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

Q4:

Determine the solution set of the equation l o g l o g 4 𝑥 𝑥 + 2 5 4 = 1 0 in .

  • A { 5 }
  • B { 1 0 }
  • C { 9 }
  • D { 1 0 2 4 }
  • E { 2 0 }

Q5:

Solve l o g l o g 2 7 𝑥 = 1 4 9 , where 𝑥 .

  • A 4
  • B4
  • C2
  • D 1 4
  • E 1 4

Q6:

Find the solution set of l o g ( 1 0 9 0 ) + 𝑥 3 = 0 𝑥 in .

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

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

Find the solution set of 2 + 2 = 7 2 𝑥 9 𝑥 in .

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

Q9:

Solve 𝑥 6 𝑥 + 8 = 0 l o g l o g 5 2 5 , where 𝑥 .

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

Q10:

Determine the solution set of the equation l o g l o g 3 2 4 3 5 𝑥 + 𝑥 + 3 = 0 in .

  • A 1 2 7
  • B 3 3
  • C { 2 7 }
  • D 1 3 3

Q11:

Find the solution set of l o g l o g 2 4 𝑥 = ( 3 𝑥 + 2 8 ) in .

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

Q12:

Find the solution set of 𝑥 + 2 𝑥 1 6 = 5 l o g l o g 4 4 in .

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

Q13:

Determine the solution set of the equation l o g l o g 4 4 𝑥 1 𝑥 = 8 3 in .

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

Q14:

Find all possible values of 𝑥 for which 𝑥 = 6 4 𝑥 l o g 2 𝑥 1 .

  • A32
  • B8 or 1 4
  • C8
  • D4 or 1 8
  • E12 or 1 1 8

Q15:

Find the solution set of 2 × 8 = 2 ( 𝑥 ) 𝑥 l o g l o g 8 2 8 4 in .

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

Q16:

Find the solution set of l o g l o g 7 𝑥 𝑥 4 9 = 1 in .

  • A { 1 , 2 }
  • B { 1 }
  • C { 1 4 }
  • D 7 , 1 4 9

Q17:

Find the solution set of l o g l o g 5 1 2 5 𝑥 = 7 2 9 in .

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

Q18:

Find the solution set of l o g l o g 4 𝑥 𝑥 + 2 5 4 = 1 0 in .

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

Q19:

Find the solution set of l o g l o g 2 𝑥 𝑥 + 2 5 2 = 1 0 in .

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

Q20:

Solve l o g l o g 9 4 𝑥 = 6 4 , where 𝑥 .

  • A27
  • B 1 7 2 9
  • C81
  • D729
  • E 1 2 7

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