Coaching Centre
Chapter 5: Logarithmic functions Notes
Calculus with the natural logarithm: log laws and equations, differentiating ln f(x), curve sketching, integrating 1/x and f'(x)/f(x), areas, and logarithms to other bases.
Sections
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5A Review of the logarithmic function base e Mastered
The inverse identities for e^x and ln x, the change-of-base formula, exponential equations that reduce to quadratics, and logarithmic scales.
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5B Differentiating logarithmic functions Mastered
The derivative of ln x, the standard form for ln f(x), using log laws to simplify before differentiating, and the product and quotient rules with logarithms.
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5C Sketching logarithmic curves Mastered
Tangents and normals to logarithmic curves, and finding stationary points and sketching curves involving ln x, paying attention to the domain.
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5D Integrating the reciprocal function Mastered
The integral of 1/x as ln|x|, the standard forms for 1/(ax+b) and f'(x)/f(x), integrals over negative intervals, and finding the integral of ln x from a given derivative.
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5E Areas with logarithmic functions Mastered
Finding areas under the hyperbola y = 1/x, between a hyperbola and a line, and areas involving y = ln x using the y-axis.
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5F Logarithmic functions to other bases Mastered
Changing log_a x to base e and differentiating logarithmic functions to any base, including with the chain rule.