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Chapter 9. Exponential and Logarithmic Functions. Chapter Sections. 9.1 – C omposite and Inverse Functions 9.2 – Exponential Functions 9.3 – Logarithmic Functions 9.4 – Properties of Logarithms 9.5 – Common Logarithms 9.6 – Exponential and Logarithmic Equations

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## Exponential and Logarithmic Functions

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**Chapter 9**Exponential and Logarithmic Functions**Chapter Sections**9.1 – Composite and Inverse Functions 9.2 – Exponential Functions 9.3 – Logarithmic Functions 9.4 – Properties of Logarithms 9.5 – Common Logarithms 9.6 – Exponential and Logarithmic Equations 9.7 – Natural Exponential and Natural Logarithmic Functions**Solve Exponential and Logarithmic Equations**Properties for Solving Exponential and Logarithmic Equations If x = y, then ax = ay. If ax = ay, then x = y. If x = y, then logbx = logby (x > 0, y > 0). If logbx=logby, then x = y (x > 0, y > 0).**Solve Exponential and Logarithmic Equations**Example Solve the equation . Property 6b**Solve Exponential and Logarithmic Equations**Example Solve Property 6d**Solve Applications**Example If there are initially 1000 bacteria in a culture, and the number of bacteria doubles each hour, the number of bacteria after t hours can be found by the formula How long will it take for the culture to grow to 30,000 bacteria? continued**Solve Applications**We want to find the value for t. To accomplish this we will use logarithms. Begin by taking the logarithm of both sides of the equation. continued**Solve Applications**It will take about 4.91 hours for the culture to grow 30,000 bacteria.

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