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.

  • A 𝑚 = 3 , 𝑛 = 4
  • B 𝑚 = 2 , 𝑛 = 4
  • C 𝑚 = 2 , 𝑛 = 4
  • D 𝑚 = 3 , 𝑛 = 4

Q3:

Use the graph to solve the following system of equations:

𝑦 = 3 + 2 ,

𝑦 = 1 5 5 .

  • A 𝑥 = 0 and 𝑦=5
  • B 𝑥 = 1 0 and 𝑦=5
  • C 𝑥 = 1 0 and 𝑦=10
  • D 𝑥 = 5 and 𝑦=10
  • E 𝑥 = 5 and 𝑦=5

Q4:

Use the graph to solve the following system of equations:

𝑦 = 4 5 1 3 ,

𝑦 = 5 .

  • A 𝑥 = 2 and 𝑦=5
  • B 𝑥 = 5 and 𝑦=2.5
  • C 𝑥 = 1 and 𝑦=5
  • D 𝑥 = 5 and 𝑦=1
  • E 𝑥 = 5 and 𝑦=2

Q5:

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

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

Q6:

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

  • A 3 , 1 7 3
  • B 9 4 , 1 1 1 2
  • C 4 9 , 1 1 1 2
  • D 1 3 , 1 7 3

Q7:

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

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

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