Worksheet: Solving Exponential Equations Using Exponent Properties

In this worksheet, we will practice solving exponential equations using the properties of exponents.

Q1:

Given that 2=32, find the value of 𝑥.

Q2:

Given that 7=49 and 4=64, find the value of 𝑥𝑦.

Q3:

Given that 8=4=64, find the value of 𝑦+𝑧.

Q4:

Find the solution set of 59=125729.

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

Q5:

Find the solution set of 4=0.25 in .

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

Q6:

Find the solution set of 2=4 in .

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

Q7:

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

Q8:

Find the value of 𝑥 for which 1625=45.

Q9:

Given that 5=25, find the value of 𝑥.

Q10:

Given that 125×2=8×5, find the value of 𝑥.

Q11:

Determine the solution set of 2=12.

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

Q12:

Determine the solution set of 𝑥=6.

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

Q13:

Find the solution set of 2=8||.

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

Q14:

Given that 5×6=216125, find the value of 𝑥.

Q15:

Find the value of 𝑥 for which 35=279.

Q16:

Find the solution set of 3=9 in .

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

Q17:

Given that 4=16||, what are the possible value of 𝑥?

  • A0
  • B2
  • C 2 , 2
  • D 2

Q18:

Determine the solution set of 5×6=125216.

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

Q19:

Given that 625×3630×5=18, find the value of 𝑦.

Q20:

Find the value of 𝑥 for which 56=2536.

Q21:

Solve 5×6=2536.

Q22:

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

  • A 2 or 0
  • B 1 or 0
  • C2 or 0
  • D2

Q23:

Find the solution set of 22=448 in .

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

Q24:

Given that 3=81, find the value of 𝑥.

Q25:

Given that 45=64125, determine the value of 𝑥.

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