Video of the lecture.
Handwritten notes from the lecture.
Waiting room video: How to use a slide rule.

Started off by reminiscing how, in primary school, we used lograithms from log tables to help us dividing one number by another. Went on to reminisce how, in secondary school, we used the logarithmic scale on a slide rule to help us dividing one number by another. Showed this Youtube clip on slide rules: How to use a slide rule

Defined the natural logarithm Ln(x) (often written as log_e(x) ) as the area under the curve y=1/t from t=1 to t=x for x≥1. For x between 0 and 1, defined Ln(x) to be the negative of the area under the curve y=1/t from t=1 to t=x. Then showed that Ln(x) has the properties required of a logarithm.

Ended up explaining how taking logarithms can simplify certain otherwise complicated calculations of derivatives.

See Appendix G (page A50) in Stewart for more details on the definition of a logarithm as the area under the curve y=1/t .

See Section 3.6 in Stewart for more examples of logarithmic differentiation.