Worksheet: Exponential Equations with Like Bases

In this worksheet, we will practice solving exponential equations by forming alike bases.

Q1:

Given that 2 = 3 2 , find the value of 𝑥 .

Q2:

Given that 7 = 4 9 and 4 = 6 4 , find the value of 𝑥 𝑦 .

Q3:

Given that 8 = 4 = 6 4 𝑦 𝑧 , find the value of 𝑦 + 𝑧 .

Q4:

Find the solution set of 5 9 = 1 2 5 7 2 9 .

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

Q5:

Given that 6 = 6 × 3 , find the value of 𝑥 correct to the nearest hundredth.

Q6:

Find the solution set of 4 = 0 . 2 5 𝑥 2 𝑥 2 in .

  • A { 1 , 1 }
  • B { 1 }
  • C { 0 , 1 }
  • D { 1 }

Q7:

Find the solution set of the equation ( 𝑥 + 8 ) = 3 2 5 in .

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

Q8:

Find the solution set of 2 = 4 in .

  • A { 8 , 4 }
  • B { 8 , 4 }
  • C { 8 , 4 }
  • D { 8 , 4 }

Q9:

Find the value of 𝑥 for which 8 = 2 . Give your answer to the nearest tenth.

Q10:

Given that 3 = 2 7 and 3 = 8 1 , find the value of 𝑥 and the value of 𝑦 .

  • A 𝑥 = 3 , 𝑦 = 4
  • B 𝑥 = 1 , 𝑦 = 3
  • C 𝑥 = 9 , 𝑦 = 4
  • D 𝑥 = 3 , 𝑦 = 1
  • E 𝑥 = 3 , 𝑦 = 1

Q11:

Find the value of 𝑥 for which 1 6 2 5 = 4 5 .

Q12:

Given that 5 = 2 5 , find the value of 𝑥 .

Q13:

Given that 1 2 5 × 2 = 8 × 5 , find the value of 𝑥 .

Q14:

Determine the solution set of 2 = 1 2 ( ) .

  • A { 8 , 1 9 2 , 2 }
  • B { 1 3 , 1 }
  • C { 2 6 , 2 }
  • D { 1 3 , 1 }
  • E { 1 6 9 , 1 }

Q15:

Determine the solution set of 𝑥 = 6 .

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

Q16:

Find the solution set of 2 = 8 | | .

  • A 5 6
  • B 4 3
  • C 3 4
  • D 6 5

Q17:

Given that 5 × 6 = 2 1 6 1 2 5 , find the value of 𝑥 .

Q18:

Find the value of 𝑥 for which 3 5 = 2 7 9 .

Q19:

Find the solution set of 3 = 9 in .

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

Q20:

Given that 4 = 1 6 | | , what are the possible value of 𝑥 ?

  • A 2
  • B2
  • C0
  • D 2 , 2

Q21:

Determine the solution set of 5 × 6 = 1 2 5 2 1 6 .

  • A { 3 }
  • B { 4 }
  • C { 4 }
  • D { 1 0 }

Q22:

Given that 6 2 5 × 3 6 3 0 × 5 = 1 8 , find the value of 𝑦 .

Q23:

Find the value of 𝑥 for which 5 6 = 2 5 3 6 .

Q24:

Solve 5 × 6 = 2 5 3 6 .

Q25:

Find all the values of 𝑥 which satisfy 7 = 1 ( ) .

  • A2
  • B2 or 0
  • C 1 or 0
  • D 2 or 0

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