1. Natural Logarithms Section 5.6

2. Lehmann, Intermediate Algebra, 4ed Section 5.6Slide 2 Definition of Natural Logarithm Definition: Natural Logarithm A Natural Logarithm is a logarithm with base e. We write ln(a) to represent log e (a). e ≈ 2.718281828459045… For a > 0, the equations are equivalent. Definition Property

3. Lehmann, Intermediate Algebra, 4ed Section 5.6Slide 3 Definition of Natural Logarithm Finding a Natural Logarithm Use a calculator to find ln(50). Press ln 50 ) ENTER Check solution Find ln(e 5 ). ln(e 5 ) = log e (e 5 ) = 5 Example Solution Example Solution

4. Lehmann, Intermediate Algebra, 4ed Section 5.6Slide 4 Solving Logarithmic and Exponential Equations Solving Logarithmic Equations Solve the equation. 1. Write in exponential form: e 4 = x so, x ≈ 54.5982 2. Example Solution

5. Lehmann, Intermediate Algebra, 4ed Section 5.6Slide 5 Solving Logarithmic and Exponential Equations Solving a Logarithmic Equations Check: Solution Continued

6. Lehmann, Intermediate Algebra, 4ed Solve 5e x–1 = 100. Check: Section 5.6Slide 6 Solving Logarithmic and Exponential Equations Solving an Exponential Equations Example Solution