Worksheet: Systems of Exponential Equations

In this worksheet, we will practice finding values that satisfy two exponential equations in two variables simultaneously.

Q1:

Find the solution set of 3×3=27 and 3+3=12.

  • A{(2,2),(2,2)}
  • B{(3,3),(3,3)}
  • C{(3,9),(9,3)}
  • D{(1,1),(1,1)}
  • E{(1,2),(2,1)}

Q2:

Given that 2×4=2,048 and 2×4=1,024, determine the values of 𝑚 and 𝑛.

  • A𝑚=3, 𝑛=4
  • B𝑚=2, 𝑛=4
  • C𝑚=2, 𝑛=4
  • D𝑚=3, 𝑛=4

Q3:

Use the graph to solve the following system of equations:

𝑦=3+2,

𝑦=155.

  • A𝑥=0 and 𝑦=5
  • B𝑥=10 and 𝑦=5
  • C𝑥=10 and 𝑦=10
  • D𝑥=5 and 𝑦=10
  • E𝑥=5 and 𝑦=5

Q4:

Use the graph to solve the following system of equations:

𝑦=4513,

𝑦=5.

  • A𝑥=2 and 𝑦=5
  • B𝑥=5 and 𝑦=2.5
  • C𝑥=1 and 𝑦=5
  • D𝑥=5 and 𝑦=1
  • E𝑥=5 and 𝑦=2

Q5:

Find the solution set of 8×8=512 and 8+8=72.

  • A{(7,7),(7,7)}
  • B{(28,28),(28,28)}
  • C{(8,64),(64,8)}
  • D{(1,1),(1,1)}
  • E{(1,2),(2,1)}

Q6:

Find the solution set of 216=1,296 and 3=81.

  • A3,173
  • B94,1112
  • C49,1112
  • D13,173

Q7:

Given that 3=27 and 3=81, find the value of 𝑥 and the value of 𝑦.

  • A𝑥=9, 𝑦=4
  • B𝑥=3, 𝑦=4
  • C𝑥=3, 𝑦=1
  • D𝑥=1, 𝑦=3
  • E𝑥=3, 𝑦=1

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