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.