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§ 4.6

§ 4.6. Properties of the Natural Logarithm Function. Section Outline. Properties of the Natural Logarithm Function Simplifying Logarithmic Expressions Differentiating Logarithmic Expressions Logarithmic Differentiation. Properties of the Natural Logarithm Function.

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§ 4.6

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  1. §4.6 Properties of the Natural Logarithm Function

  2. Section Outline • Properties of the Natural Logarithm Function • Simplifying Logarithmic Expressions • Differentiating Logarithmic Expressions • Logarithmic Differentiation

  3. Properties of the Natural Logarithm Function

  4. Simplifying Logarithmic Expressions EXAMPLE Write as a single logarithm. SOLUTION This is the given expression. Use LIV (this must be done first). Use LIII. Use LI. Simplify.

  5. Differentiating Logarithmic Expressions EXAMPLE Differentiate. SOLUTION This is the given expression. Rewrite using LIII. Rewrite using LI. Rewrite using LIV. Differentiate.

  6. Differentiating Logarithmic Expressions CONTINUED Distribute. Finish differentiating. Simplify.

  7. Logarithmic Differentiation

  8. Logarithmic Differentiation EXAMPLE Use logarithmic differentiation to differentiate the function. SOLUTION This is the given function. Take the natural logarithm of both sides of the equation. Use LIII. Use LI.

  9. Logarithmic Differentiation CONTINUED Use LIV. Differentiate. Solve for f΄(x). Substitute for f(x).

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