Solving exponential equations with logarithms

Solving exponential equations with logarithms

Basic Concepts: Solving for exponents, Converting from exponential form to logarithmic form
Related Concepts: Logarithmic scale: Richter scale (earthquake), Logarithmic scale: pH scale, Logarithmic scale: dB scale

Lessons


converting between exponential form and logarithmic form
  • 1.
    Solve for x x , by converting from exponential form
    to log form:
    a)
    y=5⋅2xy = 5 \cdot {2^x}

    b)
    6⋅3x=906 \cdot {3^x} = 90

  • 2.
    Let's revisit the earlier example about Bianca saving up money to buy her dream car, Mini Cooper.
    Now we are ready to find out the exact amount of time it'll take Bianca to save up $30,000:
    On Bianca's 5-year-old birthday, Bianca gets a birthday gift of $100 cash from her dad.
    Bianca's dad promises to double her money yearly if Bianca plans to not spend the
    money but instead deposits it into "daddy-super-saving-account". Will Bianca be able
    to afford her dream car, Mini Cooper, worth $30,000 when she turns 16-year-old?
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42.
Logarithmic Functions
42.1
What is a logarithm?
42.2
Converting from logarithmic form to exponential form
42.3
Evaluating logarithms without a calculator
42.4
Common logarithms
42.5
Natural log: ln
42.6
Evaluating logarithms using change-of-base formula
42.7
Converting from exponential form to logarithmic form
42.8
Solving exponential equations with logarithms
42.9
Product rule of logarithms
42.10
Quotient rule of logarithms
42.11
Combining product rule and quotient rule in logarithms
42.12
Evaluating logarithms using logarithm rules
42.13
Solving logarithmic equations
42.14
Graphing logarithmic functions
42.15
Finding a logarithmic function given its graph
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