A System of Exponential Equations
What do you do when you are given a problem that starts with a “lie” and ends with a wrong answer? We’ll go in several directions with this problem, a system of two exponential equations in two variables.
Logarithms
Logs of Negative or Complex Numbers
Last time we considered negative bases for logarithms; in that discussion it was mentioned that complex numbers can change everything. This will allow us to do things like finding logs of negative numbers; but it will also make things, well, more complex! Let’s take a look.
Why Can’t a Logarithm Have a Negative Base?
We’ve looked at the basics of logs and how they work; now we have some questions testing the limits of the definition. We’ll focus on the inverse idea of exponential functions with a negative base, looking at this from several perspectives.
Where Do Logarithms Come From?
Having answered many questions recently about logarithms, I realized we haven’t yet covered the basics of that topic. Here we’ll introduce the concept by way of its history, and subsequently we’ll explore how they work.
Advanced Logarithm Problems
(A new question of the week) Here is an interesting collection of problems involving logarithms with different bases, which require some unique thinking. And after we’d worked out a good strategy, another problem arose at a whole new level.