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Worksheet: Solving Natural Logarithmic Equations

Q1:

Solve the equation , giving your answer to three decimal places.

  • A
  • B
  • C
  • D

Q2:

Solve the equation , giving your answer to three decimal places.

  • A
  • B
  • C
  • D

Q3:

Solve the equation , giving your answer to three decimal places.

  • A
  • B
  • C
  • D

Q4:

Solve π‘₯ + 6 = 𝑒 l n π‘₯ 2 for π‘₯ , giving your answer to three decimal places.

  • A π‘₯ = 0 . 9 3 9
  • B no solution for π‘₯ ∈ 𝑅
  • C π‘₯ = βˆ’ 3 , π‘₯ = 2
  • D π‘₯ = 3 , π‘₯ = βˆ’ 2
  • E π‘₯ = βˆ’ 3 , π‘₯ = βˆ’ 2

Q5:

Use technology to plot the graphs of 𝑓 ( π‘₯ ) = 𝑒 βˆ’ π‘₯ and 𝑔 ( π‘₯ ) = | π‘₯ | l n . Find the coordinates where 𝑓 ( π‘₯ ) = 𝑔 ( π‘₯ ) if the curves intersect, giving your answer to two decimal places, if needed.

  • AThe curves do not intersect.
  • B ( 1 , 0 ) , ( 1 . 3 1 , 0 . 2 7 )
  • C ( 0 . 0 2 , 1 . 0 3 ) , ( 1 . 6 6 , 5 . 2 5 )
  • D ( 0 . 5 7 , 0 . 5 7 ) , ( 1 . 3 1 , 0 . 2 7 )
  • E ( 0 . 5 7 , 0 . 5 7 ) , ( 1 , 0 )

Q6:

Evaluate π‘š = 9 𝑒 l n 7 .

Q7:

Evaluate π‘š = βˆ’ 7 𝑒 l n 6 .