Exponential Equations

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Exponential Equations

• Like Bases

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Warm Up

• The following quadratic equation has exactly one
  solution for x. Find the value of k. Explore
  more than one method..

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Method One

• One solution indicates that the discriminant is
  equal to 0

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Method Two
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Warm Up - If 5,000 is invested at an interest
rate of 5 per year, find the amount of the
investment at the end of 5 years for the
following compounding methods

• Annually
• Monthly
• Quarterly
• Continuously

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• Annually

• Monthly

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• Quarterly

• Continuously

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Logarithmic Functions
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Logarithms

• Used to find unknown exponents in exponential
  models
• Define many measurement scales in the sciences
  such as the pH, decibel, and Richter scales.

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For any positive base b, where b?1 bx y if
and only if x logby
Exponential Form
Logarithmic Form
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Write in logarithmic form.
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Write in logarithmic form.
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Write in logarithmic form.
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Natural log
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The Natural Logarithmic Function

• The natural logarithmic function
• is the inverse of the natural exponential
  function

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Write in logarithmic form.
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Write in exponential form.
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Write in exponential form.
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Write in exponential form.
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Write in exponential form.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Find the value of x.
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Solve
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Find to the nearest thousandth using the
calculator.
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Find to the nearest thousandth using the
calculator.
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Find to the nearest thousandth using the
calculator.