Worksheet: Logarithmic Equations

In this worksheet, we will practice solving logarithmic equations using the laws of logarithms and the relationship between logarithmic and exponential functions.

Q1:

Determine the solution set of the equation l o g l o g l o g ( 𝑥 6 ) + ( 𝑥 + 6 ) = 6 4 in .

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

Q2:

Find 𝑥 such that l o g ( 4 𝑥 4 ) = 2 .

  • A 2 4
  • B24
  • C 2 6
  • D26

Q3:

Solve the equation l o g 𝑥 𝑥 2 = 1 , where 𝑥 .

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

Q4:

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

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

Q5:

Solve l o g 𝑥 2 6 𝑥 7 𝑥 + 6 = 1 , where 𝑥 .

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

Q6:

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

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

Q7:

Determine the solution set of the equation l o g l o g 𝑥 = 4 ( 𝑥 + 6 ) in .

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

Q8:

Solve l o g l o g 𝑥 8 𝑥 = 1 , where 𝑥 .

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

Q9:

Find the solution set of 3 + 2 4 3 = 2 4 4 × 3 in .

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

Q10:

Find the solution set of 4 + 2 = 5 1 6 in .

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

Q11:

Find the solution set of 3 + 2 4 3 3 = 3 6 in .

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

Q12:

What is the solution set of the equation l o g ( 9 𝑥 1 8 ) = 2 ?

  • A { 2 }
  • B 2 0 9
  • C
  • D { 3 , 6 }

Q13:

Find the solution set of 4 1 , 0 2 6 × 2 + 2 , 0 4 8 = 0 in .

  • A { 2 , 2 , 7 , 7 }
  • B { 2 , 2 }
  • C { 2 , 7 }
  • D 2 , 2

Q14:

Find the solution set of l o g l o g l o g 9 𝑥 2 7 = 2 𝑥 + 1 3 2 1 6 in .

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

Q15:

Find the solution set of l o g l o g l o g l o g 5 + 4 0 2 4 = 2 + 8 in .

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

Q16:

Determine the solution set of the equation 2 × 5 = 6 4 , 0 0 0 l o g l o g in .

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

Q17:

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

  • 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 }

Q18:

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

Q19:

Find the solution set of l o g l o g l o g l o g 2 1 6 × 8 1 = 3 6 × 𝑥 in .

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

Q20:

Solve 5 = 1 5 l o g , where 𝑥 .

  • A 6 5
  • B6
  • C1
  • D 1 6

Q21:

Solve l o g ( 2 + 5 1 0 ) = 1 0 𝑥 , where 𝑥 .

Q22:

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

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

Q23:

Solve the equation l o g 𝑥 3 5 𝑥 = 5 𝑥 , where 𝑥 .

  • A175
  • B 1 7
  • C10
  • D7
  • E30

Q24:

If 8 𝑥 + 5 𝑦 𝑥 𝑦 = 3 l o g l o g l o g , what is the value of 𝑥 𝑦 ?

  • A6
  • B 4 0 6
  • C36
  • D 6 6

Q25:

Determine the solution set of l o g 5 0 3 + 3 = l o g 8 in .

  • A { 6 }
  • B { 4 }
  • C { 9 }
  • D { 1 2 }

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