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.

  • A65
  • B{3}
  • C{6}
  • D13

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{8,192,2}
  • B{26,2}
  • C{13,1}
  • D{169,1}
  • E{13,1}

Q12:

Determine the solution set of 𝑥=6.

  • A{6,6,8,8}
  • B{6,8,8}
  • C{6,6,32,32}
  • D{6,64}
  • E{6,8}

Q13:

Find the solution set of 2=8||.

  • A56
  • B43
  • C65
  • D34

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
  • C2,2
  • D2

Q18:

Determine the solution set of 5×6=125216.

  • A{10}
  • 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.

  • A𝑥=3
  • B𝑥=1
  • C𝑥=2
  • D𝑥=3
  • E𝑥=2

Q22:

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

  • A2 or 0
  • B1 or 0
  • C2 or 0
  • D2

Q23:

Find the solution set of 22=448 in .

  • A{1}
  • B{7}
  • C{6}
  • D{14}
  • E{128}

Q24:

Given that 3=81, find the value of 𝑥.

Q25:

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

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