Worksheet: Natural Exponential Equations

In this worksheet, we will practice solving exponential equations with base e by using laws of natural exponents.

Q1:

Solve 3𝑒4=8, giving your answer correct to three decimal places.

  • A𝑥=1.386
  • B𝑥=0.981
  • C𝑥=1.946
  • D𝑥=0.288
  • E𝑥=2.485

Q2:

Find, to the nearest thousandth, the value of 𝑥 such that 𝑒=19.

Q3:

Solve 2=5𝑒 for 𝑥, giving your answer to three decimal places.

  • A𝑥=1.464
  • B𝑥=1.986
  • C𝑥=1.756
  • D𝑥=1.464
  • E𝑥=1.986

Q4:

Given that 𝑒2=1, find the value of 𝑥. If necessary, give your answer to 3 decimal places.

Q5:

Solve 2𝑒+11=18, giving your answer correct to three decimal places.

  • A𝑥=2.674
  • B𝑥=0.424
  • C𝑥=0.891
  • D𝑥=0.418
  • E𝑥=1.253

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