Exponential & Logarithmic Thinking The Math Behind Scalable Growth

Most people learn exponents and logarithms as abstract math. Leaders use them to understand growth, decay, risk, and timing. In this video, we break down the mathematics that governs: Viral growth and network effects Compound interest and long-term capital growth Decay, depreciation, and half-life Why logarithms are the key to solving for time in any growth model 00:02 - Understanding exponential and logarithmic functions and their applications. 01:55 - Understanding the laws of exponents is crucial for simplifying expressions. 05:45 - Rational exponents represent roots, simplifying calculations. 07:40 - Exponential functions show unique growth behavior compared to linear functions. 11:42 - Explores exponential decay for bases between 0 and 1. 13:52 - Logarithms are the inverse of exponential functions, reflecting their properties. 17:51 - Understanding exponential and logarithmic relationships in mathematics. 19:49 - Understanding logarithmic functions and their application in solving exponential equations. 23:28 - Isolate logarithms and convert to exponential form for solving equations. 25:19 - Logarithms cannot accept negative values due to exponential constraints. 29:04 - Exploring real-world applications of exponential and logarithmic functions. This is not formula memorization. It is decision-grade math—the tools that explain why some systems scale, others collapse, and how small changes compound into massive outcomes. If you want to understand the math behind money, markets, populations, and exponential technologies, this is where it starts.