The Quadratic Formula

The quadratic formula is one of, if not, the first “big” formulas introduced in algebra. It looks pretty daunting: Many students have get a lot of anxiety when they see this.  However, it is a powerful analytical tool that helps us find the roots, or zeros, of a quadratic function.   These are the points where … Continue reading The Quadratic Formula

The Natural Logarithm and its Rules

The rules for Natural logarithm Are the rules for natural log the same as logarithms of other bases?  Yes, all logarithms follow the same rules regardless of base.  Those are: \begin{equation} ln(ab)=ln(a)+ln(b) \end{equation} \begin{equation} ln(\frac{a}{b})=ln(a)-ln(b) \end{equation} \begin{equation} ln(b^c)=c ln(b) \end{equation} \begin{equation} ln(a)=\frac{log_b(a)}{log_b(e)} \end{equation} The natural logarithm is simply the logarithm of base e.   In other … Continue reading The Natural Logarithm and its Rules