General Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — Logarithmic function and its graphical representation

About this lesson

This unit introduces the logarithmic function as the inverse of the exponential function, focusing on converting between exponential and logarithmic forms. It covers the definition of logarithms, the common logarithm (base 10), and solving simple logarithmic equations. The unit also includes graphical representation of logarithmic functions, exploring properties like domain, range, and monotonicity, with examples using bases greater than 1 and between 0 and 1. Students practice finding values of logarithms, solving equations, and using calculators for common logarithms. The text includes exercises and examples with bases such as 2, 3, 5, and 10, and emphasizes the domain restrictions for logarithmic equations.

Main topics in this lesson

  • Definition of logarithmic function
  • Converting between exponential and logarithmic forms
  • Common logarithm (base 10)
  • Solving logarithmic equations
  • Graphical representation of logarithmic functions
  • Properties of logarithmic functions (domain, range, monotonicity)

Key terms and vocabulary

  • logarithm
  • inverse function
  • domain
  • common logarithm
  • exponential form
  • logarithmic form
  • base
  • calculator

Questions and answers on Exponents, Logarithms and their Applications — Logarithmic function and its graphical representation - practice and revision

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

1

قيمة log₇ 7 تساوي:

  • 1 0
  • 2 1
  • 3 7
  • 4 -1
2

قيمة log₄ 1 تساوي:

  • 1 0
  • 2 1
  • 3 4
  • 4 -1
3

الدالة اللوغاريتمية ص = log₀.₅ س تكون:

  • 1 متزايدة لأن الأساس بين 0 و 1
  • 2 متناقصة لأن الأساس بين 0 و 1
  • 3 ثابتة لأن الأساس بين 0 و 1
  • 4 غير معرّفة لأن الأساس بين 0 و 1
4

الدالة اللوغاريتمية ص = log₂ س تكون:

  • 1 متناقصة لأن الأساس أكبر من 1
  • 2 متزايدة لأن الأساس أكبر من 1
  • 3 ثابتة لأن الأساس أكبر من 1
  • 4 غير معرّفة لأن الأساس أكبر من 1
5

مدى الدالة اللوغاريتمية ص = log₃ س هو:

  • 1 ص > 0
  • 2 ص ≥ 0
  • 3 مجموعة الأعداد الحقيقية
  • 4 ص ≠ 0
6

مجال الدالة اللوغاريتمية ص = log₂ س هو:

  • 1 مجموعة الأعداد الحقيقية
  • 2 س > 0
  • 3 س ≥ 0
  • 4 س ≠ 0

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