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Natural Logarithms

Section 5.6. Natural Logarithms. Definition. 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. Property. Section 5.6. Slide 2. Definition of Natural Logarithm.

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Natural Logarithms

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  1. Section 5.6 Natural Logarithms

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

  3. Example Use a calculator to find ln(50). Press ln 50 ) ENTER Check solution Find ln(e5). ln(e5) = loge(e5) = 5 Solution Example Solution Section 5.6 Slide 3 Definition of Natural Logarithm Finding a Natural Logarithm

  4. Example Solve the equation. 1. Write in exponential form: e4 = x so, x ≈ 54.5982 2. Solution Section 5.6 Slide 4 Solving Logarithmic and Exponential Equations Solving Logarithmic Equations

  5. Solution Continued Check: Section 5.6 Slide 5 Solving Logarithmic and Exponential Equations Solving a Logarithmic Equations

  6. Example Solve 5ex–1 = 100. Check: Solution Section 5.6 Slide 6 Solving Logarithmic and Exponential Equations Solving an Exponential Equations

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