General Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — Some properties of logarithms

About this lesson

This unit covers properties of logarithms and their applications. It begins by listing several properties: log base a of a equals 1, log base a of 1 equals 0, the multiplication property (log xy = log x + log y), the division property (log x/y = log x - log y), the power property (log x^n = n log x), the change of base property, and the multiplicative inverse property. Each property is stated with examples and some proofs are sketched. The unit then demonstrates how to simplify logarithmic expressions using these properties, and how to solve logarithmic equations by applying the properties and converting between logarithmic and exponential forms. It also shows how to solve exponential equations by taking logarithms of both sides and using a calculator. The unit includes worked examples, 'try to solve' exercises, and a set of exercises at the end. The text also includes an introduction to a separate unit on calculus, but that is not part of this unit's content.

Main topics in this lesson

  • Properties of logarithms
  • Simplifying logarithmic expressions
  • Solving logarithmic equations
  • Solving exponential equations using logarithms
  • Using a calculator for exponential equations

Key terms and vocabulary

  • logarithm
  • logarithmic equation
  • exponential function
  • properties of logarithms
  • multiplication property
  • division property
  • power property
  • change of base
  • multiplicative inverse
  • simplifying logarithmic expressions
  • solving logarithmic equations
  • solving exponential functions

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

حل المعادلة \(\log_4 x = 3\) هو:

  • 1 64
  • 2 12
  • 3 81
  • 4 7
2

قيمة \(\log_9 3\) تساوي:

  • 1 \(\frac{1}{2}\)
  • 2 3
  • 3 9
  • 4 \(\frac{1}{3}\)
3

إذا كان \(\log 2 = 0.301\) فإن \(\log 8\) يساوي:

  • 1 0.903
  • 2 0.602
  • 3 2.408
  • 4 1.204
4

قيمة \(\log_5 125 + \log_5 1\) تساوي:

  • 1 3
  • 2 4
  • 3 125
  • 4 0
5

إذا كان \(\log_x 49 = 2\) فإن قيمة \(x\) تساوي:

  • 1 7
  • 2 24.5
  • 3 49
  • 4 14
6

قيمة \(\log_2 6 + \log_2 4 - \log_2 3\) تساوي:

  • 1 3
  • 2 2
  • 3 5
  • 4 1

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