Worksheet: Natural Logarithmic Equations

In this worksheet, we will practice solving natural logarithmic equations using natural base exponential functions.

Q1:

Find the solution set of the equation l n l n 𝑒 = 3 7 , giving your answer to three decimal places.

  • A { 1 . 5 4 2 }
  • B { 0 . 1 7 1 }
  • C { 5 . 8 3 8 }
  • D { 0 . 6 4 9 }

Q2:

Solve 𝑥 + 6 = 𝑒 l n for 𝑥 , giving your answer to three decimal places.

  • A 𝑥 = 3 , 𝑥 = 2
  • B 𝑥 = 0 . 9 3 9
  • C 𝑥 = 3 , 𝑥 = 2
  • D 𝑥 = 3 , 𝑥 = 2
  • E no solution for 𝑥 𝑅

Q3:

Evaluate 𝑚 = 9 𝑒 l n .

Q4:

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

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

Q5:

Find the solution set of the equation l n l n 𝑒 = 5 7 , giving your answer to three decimal places.

  • A { 1 . 5 5 7 }
  • B { 0 . 4 1 1 }
  • C { 0 . 6 4 2 }
  • D { 2 . 4 3 2 }

Q6:

Find the solution set of the equation l n l n 𝑒 = 3 4 , giving your answer to three decimal places.

  • A { 0 . 4 8 1 }
  • B { 2 . 0 7 9 }
  • C { 1 . 0 8 2 }
  • D { 0 . 9 2 4 }

Q7:

Evaluate 𝑚 = 7 𝑒 l n .

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