UPDATE: I had made a notation error in the definition of the logarithmic function at around time 1:18 to 1:30 but the rest of the video is still correct. The link to the corrected definition is shown below:

Definition of Inverse Functions and Logarithms:

Logs are really useful in all of math and calculus and understanding them is very important to understand most of the complex mathematical concepts that have been developed over the years. They are quite basic in their definition and with a full understanding of them, they can be applied in many real world applications.

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Logarithmic Functions and their Properties: An Introduction

Definition of Logarithms

MES Correction: Note that the above definition has the wrong notation. It should be y = a^x --> y = log_ax as outlined in my later video:

Log Properties / Laws

Property 1: log_aa^x = x

Property 2: a^log_ax = x

Property 3: log_ay + log_ax = log_a(y·x)

Property 4: log_ay - log_ax = log_a(y/x)

Property 5: y = log_ax^R = R·log_ax

Property 6: Change of Base Formula: log_ax = log_bx / log_ba