1. 9.5 BASE E AND NATURAL LOGS

2. NATURAL BASE EXPONENTIAL FUNCTION An exponential function with base e  e is the irrational number 2.71828… *These are used extensively in science to model quantities that grow and decay continuously Calculator button exex

3. EVALUATE TO FOUR DECIMAL PLACES 1. e 2 2. e -1.3 3. e 1/2

4. THE LOG WITH BASE E IS A NATURAL LOG Written as : ln y=ln x is the inverse of y = e x All properties for logs apply the same way to natural logs Calculator button lnx

5. EXAMPLES Use calculator to evaluate to four decimal places 4. ln45. ln0.056. ln7

6. EXAMPLE Write an equivalent exponential or log equation to the given equation. 7. e x =58. lnx≈0.6931

7. REMEMBER….. All log properties apply to natural logs Do the same thing for ln problems that you do for log problems Let’s solve!!!!!!!!!

8. EXAMPLE 9 Solve e 4x =120 and round to four decimal places

9. EXAMPLE 10 EXAMPLE 11 e x-2 + 4 4

10. EXAMPLE 12EXAMPLE 13 ln5x+ln3x>92e 3x + 5 =2