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Lesson: Exponential Equations with Like Bases

Sample Question Videos

Worksheet • 25 Questions • 4 Videos

Q1:

Given that 7 = 4 9 π‘₯ and 4 = 6 4 𝑦 , find the value of π‘₯ 𝑦 .

Q2:

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

Q3:

Find the solution set of 2 = 8 | 8 π‘₯ βˆ’ 1 2 | 4 π‘₯ βˆ’ 4 .

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

Q4:

Given that 5 Γ— 6 = 2 1 6 1 2 5 π‘₯ βˆ’ 6 6 βˆ’ π‘₯ , find the value of π‘₯ .

Q5:

Find the value of π‘₯ for which ο€Ό 3 5  = 2 7 9 2 π‘₯ βˆ’ 4 .

Q6:

Given that 8 1 Γ— 4 = 2 5 6 Γ— 3 π‘₯ + 6 π‘₯ + 6 , find the value of π‘₯ .

Q7:

Given that 1 2 5 Γ— 2 = 8 Γ— 5 π‘₯ βˆ’ 4 π‘₯ βˆ’ 4 , find the value of π‘₯ .

Q8:

Find the solution set of 3 = 9 π‘₯ βˆ’ 3 6 π‘₯ βˆ’ 3 6 2 2 in ℝ .

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

Q9:

Given that 4 = 1 6 | π‘₯ | , what are the possible value of π‘₯ ?

  • A 2 , βˆ’ 2
  • B2
  • C0
  • D βˆ’ 2

Q10:

Determine the solution set of 2 Γ— 3 = 4 9 π‘₯ βˆ’ 5 5 βˆ’ π‘₯ .

  • A { 7 }
  • B { βˆ’ 3 }
  • C { 3 }
  • D { 2 }

Q11:

Given that 6 2 5 Γ— 3 6 3 0 Γ— 5 = 1 8 π‘₯ π‘₯ 2 π‘₯ 2 π‘₯ 𝑦 βˆ’ 8 , find the value of 𝑦 .

Q12:

Find the value of π‘₯ for which ο€Ό 6 5  = 2 1 6 1 2 5 3 π‘₯ βˆ’ 3 .

Q13:

Solve 8 Γ— 2 = 4 π‘₯ βˆ’ π‘₯ .

Q14:

Find all the values of π‘₯ which satisfy 7 = 1 π‘₯ ( π‘₯ + 2 ) .

  • A βˆ’ 2 or 0
  • B2 or 0
  • C βˆ’ 1 or 0
  • D2

Q15:

Find the solution set of 2 βˆ’ 2 = 4 4 8 π‘₯ + 2 π‘₯ βˆ’ 1 in ℝ .

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

Q16:

Given that 2 = 1 6 π‘₯ + 8 , find the value of π‘₯ .

Q17:

Given that ο€Ό 4 5  = 6 4 1 2 5 π‘₯ + 7 , determine the value of π‘₯ .

Q18:

If 2 5 Γ— 7 3 5 = 1 2 5 π‘₯ π‘₯ π‘₯ , then what is the value of π‘₯ ?

Q19:

Given that 𝑓 ( π‘₯ ) = 6 π‘₯ βˆ’ 1 2 , find the solution set of the equation 𝑓 ( π‘₯ + 8 ) = 1 3 6 .

  • A { 2 }
  • B { βˆ’ 2 }
  • C { βˆ’ 2 2 }
  • D { 1 8 }

Q20:

Find the solution set of 4 Γ— 2 = 1 2 π‘₯ + 4 in ℝ .

  • A { βˆ’ 7 }
  • B { βˆ’ 1 }
  • C { 7 }
  • D { 1 }

Q21:

Given that 6 Γ— 2 7 7 2 9 Γ— 2 Γ— 7 2 9 = 2 3 𝑛 𝑛 + 2 2 𝑛 𝑛 , find the value of 𝑛 , where 𝑛 ∈ β„€ .

Q22:

Determine the solution set of π‘₯ = 5 π‘₯ βˆ’ 6 4 π‘₯ βˆ’ 6 4 2 2 .

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

Q23:

Determine the solution set of π‘₯ = 8 π‘₯ βˆ’ 3 6 π‘₯ βˆ’ 3 6 2 2 .

  • A { 8 , βˆ’ 8 , 6 , βˆ’ 6 }
  • B { 8 , βˆ’ 8 , 1 8 , βˆ’ 1 8 }
  • C { 8 , 6 , βˆ’ 6 }
  • D { 8 , 3 6 }
  • E { 8 , 6 }

Q24:

Find the value of π‘₯ for which 2 5 4 = ο€Ό 5 2  π‘₯ .

Q25:

Determine the solution set of 4 = ο€Ό 1 4  ( π‘₯ + 8 ) 6 π‘₯ 2 .

  • A { βˆ’ 4 , βˆ’ 2 }
  • B { 4 , 2 }
  • C { βˆ’ 1 6 , βˆ’ 8 }
  • D { 2 5 6 , 1 6 }
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