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.

  • A 𝑥 = 1 . 3 8 6
  • B 𝑥 = 0 . 9 8 1
  • C 𝑥 = 1 . 9 4 6
  • D 𝑥 = 0 . 2 8 8
  • E 𝑥 = 2 . 4 8 5

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.

  • A 𝑥 = 1 . 4 6 4
  • B 𝑥 = 1 . 9 8 6
  • C 𝑥 = 1 . 7 5 6
  • D 𝑥 = 1 . 4 6 4
  • E 𝑥 = 1 . 9 8 6

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.

  • A 𝑥 = 2 . 6 7 4
  • B 𝑥 = 0 . 4 2 4
  • C 𝑥 = 0 . 8 9 1
  • D 𝑥 = 0 . 4 1 8
  • E 𝑥 = 1 . 2 5 3

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