Pure Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — The logarithmic function and its graph

About this lesson

This unit introduces the logarithmic function as the inverse of the exponential function, focusing on definitions, conversions between exponential and logarithmic forms, and solving simple exponential equations. It covers the common logarithm (base 10), evaluating logarithms, and determining the domain of logarithmic functions. The unit also includes graphical representation of logarithmic functions for bases greater than 1 and between 0 and 1, using reflection in the line y=x to show the inverse relationship. Practical applications involve using a scientific calculator to find logarithm values and solving equations with logarithms. Real-world contexts include education, where student retention scores are modeled by logarithmic functions over time. By the end, students should be able to convert between forms, evaluate logarithms, solve basic logarithmic equations, graph logarithmic functions, and apply these skills to word problems.

Main topics in this lesson

  • Definition of logarithmic function
  • Inverse relationship with exponential function
  • Conversion between exponential and logarithmic forms
  • Common logarithms (base 10)
  • Evaluating logarithms
  • Solving logarithmic equations
  • Graphical representation of logarithmic functions
  • Using scientific calculator for logarithms
  • Applications in education (retention scores)

Key terms and vocabulary

  • Logarithm
  • Inverse function
  • Exponential function
  • Logarithmic function
  • Common logarithm
  • Base
  • Domain
  • Range
  • Graphical representation
  • Scientific calculator

Questions and answers on Exponents, Logarithms and their Applications — The logarithmic function and its graph - 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

إذا كان logₐ 81 = 4، فإن قيمة a تساوي:

  • 1 3
  • 2 9
  • 3 4
  • 4 27
2

مجال الدالة f(x) = log(x + 2) هو:

  • 1 x > −2
  • 2 x > 2
  • 3 x ≥ −2
  • 4 x < −2
3

قيمة log₇ 7 تساوي:

  • 1 1
  • 2 0
  • 3 7
  • 4 49
4

حل المعادلة 2ˣ = 32 هو:

  • 1 5
  • 2 4
  • 3 6
  • 4 16
5

أي العبارات التالية صحيحة بالنسبة لدالة اللوغاريتم عندما يكون الأساس أكبر من 1؟

  • 1 الدالة متزايدة وتمثل انعكاس الدالة الأسية في y = x
  • 2 الدالة متناقصة وتمثل انعكاس الدالة الأسية في y = x
  • 3 الدالة ثابتة ولا تتغير قيمتها
  • 4 الدالة غير معرفة لأي قيمة موجبة
6

إذا كانت الدالة f(x) = log(x)، فما قيمة x التي تجعل f(x) = 2؟

  • 1 100
  • 2 20
  • 3 10
  • 4 1000

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