Introduction to Logarithms (DP IB Applications & Interpretation (AI)): Revision Note

Introduction to Logarithms

What are logarithms?

• A logarithm is the inverse of a power

  • If then  where , ,

    • It turns the power, , into the subject of the equation

• The number is called the base of the logarithm

  • is pronounced "log base of "

  • e.g.  asks "what power of 5 gives you 125?"

    • The answer is 3, as

    • so

• Two important cases are:

  • The natural logarithm,

    • where is the mathematical constant 2.718…

    • often called Euler's number

  • Logarithms of base 10,

    • They are written with no base

Why use logarithms?

• Equations where is in the power are called exponential equations

  • Some can be solved easily by inspection (seeing the answer)

    • For example, is solved by seeing that

  • Others cannot be seen

    • For example,

  • These must be solved using logarithms by making the subject

    • means

    • Type this into your GDC to get