Pure Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — Some properties of logarithms

About this lesson

This unit covers properties of logarithms, including the multiplication, division, power, base changing, and multiplicative inverse properties. It also teaches how to simplify logarithmic expressions, solve logarithmic equations, and solve exponential equations using logarithms and a scientific calculator. Applications include the Richter scale for earthquake magnitude and a population growth model. By the end, students should be able to apply logarithm properties, solve equations, and use calculators for exponential equations.

Main topics in this lesson

  • Properties of logarithms
  • Simplifying logarithmic expressions
  • Solving logarithmic equations
  • Solving exponential equations using logarithms
  • Applications of logarithms (Richter scale, population growth)

Key terms and vocabulary

  • Logarithmic equations
  • Richter scale
  • Multiplication property
  • Division property
  • Power property
  • Base changing property
  • Multiplicative inverse property
  • Reference intensity

Questions and answers on Exponents, Logarithms and their Applications — Some properties of logarithms - practice and revision

Multiple choice questions on this lesson in Pure Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

حل المعادلة 3ˣ = 81 هو:

  • 1 x = 4
  • 2 x = 3
  • 3 x = 27
  • 4 x = 5
2

قيمة log₃ 81 − log₃ 27 تساوي:

  • 1 1
  • 2 3
  • 3 27
  • 4 0
3

إذا كانت log₂ x + log₂ 4 = 5 فإن قيمة x تساوي:

  • 1 8
  • 2 4
  • 3 16
  • 4 2
4

قيمة log₁₀ 1000 تساوي:

  • 1 3
  • 2 2
  • 3 10
  • 4 100
5

قيمة log₂ 64 تساوي:

  • 1 6
  • 2 5
  • 3 8
  • 4 32
6

حل المعادلة 2ˣ = 32 باستخدام اللوغاريتمات هو:

  • 1 x = 5
  • 2 x = 4
  • 3 x = 6
  • 4 x = 16

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