Worksheet: Exponential Inequalities

In this worksheet, we will practice solving the exponential inequalities whose bases can all be converted to the same value.

Q1:

It is known that 16 is in the interval [0.25,0.5]. In what interval does 𝑥 lie?

  • A[0.25,0.5]
  • B[0.5,0.25]
  • C[0.5,0.5]
  • D[0.25,0.5]
  • E[0.5,0.25]

Q2:

If 13>13, which of the following must be true about 𝑥 and 𝑦?

  • A𝑥=𝑦
  • B𝑥>𝑦
  • C𝑦>𝑥

Q3:

Find the values of 𝑥 that satisfy the following inequality: 4>8.

  • A𝑥<2
  • B𝑥<1
  • C𝑥>2
  • D𝑥>1
  • E𝑥<0

Q4:

Find all the values of 𝑥 that satisfy the following inequality: 2>2.

  • A𝑥<1
  • B𝑥>3
  • C𝑥<3
  • D𝑥<0
  • E𝑥>1

Q5:

Suppose that 𝑎<𝑥<𝑏 is the solution of the following inequality: 13>19. Find 𝑏𝑎.

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