Logarithms | Log laws, change of base, equations

Welcome to Day 7 of the 50 Days of Tutelage series. Logarithms are simply the inverse of exponents. This lesson breaks down the fundamental rules of logs and shows you how to use them to solve equations where the unknown variable is an exponent. We walk through the core concepts in a simple, step-by-step flow: • What is a Logarithm?: Understanding the basic definition—if b^y = x, then \log_b(x) = y. We look at how to switch between exponential form and logarithmic form. • The Core Laws of Logs: Mastering the main operational rules: the Product Rule (\log xy = \log x + \log y), the Quotient Rule (\log \frac{x}{y} = \log x - \log y), and the Power Rule (\log x^k = k \log x). • Special Bases: Differentiating between Common Logarithms (Base 10) and Natural Logarithms (Base e, written as \ln). • Change of Base Formula: How to rewrite a logarithm to any base so you can easily calculate or simplify it (\log_b a = \frac{\log_c a}{\log_c b}). #Mathematics #Logarithms #Algebra #PureMath #STEM #50DaysOfTutelage