Worksheet: Natural Logarithmic Equations

In this worksheet, we will practice solving natural logarithmic equations using the laws of natural logarithms.

Q1:

Find the solution set of the equation lnln𝑒=37, giving your answer to three decimal places.

  • A{0.171}
  • B{0.649}
  • C{1.542}
  • D{5.838}

Q2:

Solve 𝑥+6=𝑒ln for 𝑥, giving your answer to three decimal places.

  • A𝑥=3,𝑥=2
  • Bno solution for 𝑥𝑅
  • C𝑥=0.939
  • D𝑥=3,𝑥=2
  • E𝑥=3,𝑥=2

Q3:

Evaluate 𝑚=9𝑒ln.

Q4:

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

  • AThe curves do not intersect.
  • B(0.02,1.03), (1.66,5.25)
  • C(1,0), (1.31,0.27)
  • D(0.57,0.57), (1.31,0.27)
  • E(0.57,0.57), (1,0)

Q5:

Find the solution set of the equation lnln𝑒=57, giving your answer to three decimal places.

  • A{0.642}
  • B{2.432}
  • C{0.411}
  • D{1.557}

Q6:

Find the solution set of the equation lnln𝑒=34, giving your answer to three decimal places.

  • A{1.082}
  • B{2.079}
  • C{0.481}
  • D{0.924}

Q7:

Evaluate 𝑚=7𝑒ln.

Q8:

Solve lnln9=74 for 𝑥, giving your answer to the nearest hundredth.

  • A{1.57}
  • B{1.01}
  • C{10.96}
  • D{0.28}

Q9:

Find the set of all 𝑥 such that lnlnln(8𝑥7)+(6𝑥1)=7.

  • A2524
  • B2524
  • C2524,0
  • D78,16

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