Evaluating logarithms using change-of-base formula

Evaluating logarithms using change-of-base formula

Basic Concepts: Converting from logarithmic form to exponential form, Evaluating logarithms without a calculator, Common logarithms
Related Concepts: Logarithmic scale: Richter scale (earthquake), Logarithmic scale: pH scale, Logarithmic scale: dB scale

Lessons

• change-of-base rule:
log⁡ba=log⁡xalog⁡xb=log⁡alog⁡b \log_ba = \frac{\log_xa}{\log_xb} = \frac{\log a}{\log b}

• common logarithms:
log with base ‘‘10" ``10"
example: log⁡3=log⁡103 \log3 = \log_{10}3
example: log⁡x=log⁡10x \log x = \log_{10}x
  • 1.
    How to apply ‘‘ `` change-of-base rule""

    Express log⁡53 \log_53 in three different ways.
  • 2.
    Using a calculator, evaluate the following logarithms
    by applying ‘‘ `` change-of-base rule":":
    a)
    log⁡53\log_53

    b)
    log⁡7416\log_7\sqrt{416}

    c)
    log⁡2725\log_2\frac{7}{25}

    d)
    6log⁡4999 \log_4999

  • 3.
    Using a calculator, solve for x x to the nearest hundredth.
    a)
    log⁡6x=log78\log_6x = log_7 8

    b)
    log⁡235=logx0.104\log_{23}5 = log_x\sqrt{0.104}

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10.
Logarithmic Functions
10.1
What is a logarithm?
10.2
Converting from logarithmic form to exponential form
10.3
Evaluating logarithms without a calculator
10.4
Common logarithms
10.5
Natural log: ln
10.6
Evaluating logarithms using change-of-base formula
10.7
Converting from exponential form to logarithmic form
10.8
Solving exponential equations with logarithms
10.9
Product rule of logarithms
10.10
Quotient rule of logarithms
10.11
Combining product rule and quotient rule in logarithms
10.12
Evaluating logarithms using logarithm rules
10.13
Solving logarithmic equations
10.14
Graphing logarithmic functions
10.15
Finding a logarithmic function given its graph
NZ Year 11 Maths
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