logarithm Archives - Infinity is Really Big

September 26, 2019September 26, 2019

Transformations of Functions

Calculus 1, Lectures 6A through 7B

Visual for the fact that $\log_{2}(2x)=\log_{2}(x)+\log_{2}(2)=\log_{2}(x)+1$ in terms of transformations of functions.

\log_{2}(2x)=\log_{2}(x)+\log_{2}(2)=\log_{2}(x)+1 — Visual for the fact that $\log_{2}(2x)=\log_{2}(x)+\log_{2}(2)=\log_{2}(x)+1$ in terms of transformations of functions.

In the 1600’s, algebra and geometry got “married” to create a new subject called analytic geometry. Insights in either branch led to insights in the other. This has been very fruitful over the years.

The symbiosis between these subjects can be especially … Read the rest

January 10, 2019July 4, 2019

Financial Mathematics Tools: Substitutions, Quadratic Formula, Logarithms, and “Functional-Thinking”

The quadratic formula

Useful pre-university mathematics is not restricted to arithmetic, percentages, and basic algebra.

Functional-thinking is one key to doing many other useful things. Tools such as substitutions, the quadratic formula, and logarithms also come in handy.

These tools are used in engineering and science. For example, in the evaluation of useful integrals (such as those that come up in … Read the rest