Exponential Equations Like Bases. Warm Up  The following quadratic equation has exactly one solution for x. Find the value of k. Explore more than one.

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Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.

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Presentation transcript:

Exponential Equations Like Bases

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

Method One  One solution indicates that the discriminant is equal to 0:

Method Two

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

 Annually:  Monthly:

 Quarterly:  Continuously

Logarithmic Functions

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

For any positive base b, where b≠1: b x = y if and only if x = log b y Exponential FormLogarithmic Form

Write in logarithmic form.

Natural log

The Natural Logarithmic Function  The natural logarithmic function is the inverse of the natural exponential function

Write in logarithmic form.

Write in exponential form.

Find the value of x.

Solve

Find to the nearest thousandth – using the calculator.