Lesson Worksheet: Solving Exponential Equations Using Logarithms Mathematics • 10th Grade

In this worksheet, we will practice using logarithms to solve exponential equations.

Q1:

Fill in the blank: If 𝑎=𝑏, then 𝑥=.

  • Aln𝑎
  • Blog𝑎
  • Cln𝑏
  • D𝑎𝑏log
  • Elog𝑏

Q2:

Solve 3=11 for 𝑥, giving your answer to three decimal places.

  • A𝑥=0.497
  • B𝑥=2.183
  • C𝑥=3.667
  • D𝑥=0.564
  • E𝑥=0.273

Q3:

Use a calculator to find the value of 𝑥 for which 9=8. Give your answer correct to two decimal places.

Q4:

Find the solution set to the equation 15=64. Give your answer to three decimal places.

  • A{1.536}
  • B{0.651}
  • C{0.234}
  • D{4.267}

Q5:

Use a calculator to find the value of 𝑥 for which 23=1.7602. Give your answer correct to two decimal places.

Q6:

Solve 13.5=5.6, giving your answer to the nearest 2 decimal places.

Q7:

Solve 23=54 for 𝑥, giving your answer to three decimal places.

  • A𝑥=3.793
  • B𝑥=3.185
  • C𝑥=0.369
  • D𝑥=0.369
  • E𝑥=3.185

Q8:

Find, to the nearest hundredth, the value of 𝑥 for which 2=9.

Q9:

Use a calculator to find the value of 𝑥 for which 3=8. Give your answer correct to two decimal places.

Q10:

Use a calculator to find the value of 𝑥 for which 2×7=16×7. Give your answer correct to two decimal places.

This lesson includes 17 additional questions and 153 additional question variations for subscribers.

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