How to Solve Logarithmic Equations: Definition and Properties
TL;DR: Logarithmic equations look intimidating until you spot the rhythm. Combine the logs on each side first, then drop the log to leave plain algebra, solve, and — here is the step everyone forgets — check your answers against the domain. Logs only accept positive inputs, so any solution that sneaks in a negative or […]
How to Graph Logarithmic Functions?
TL;DR: A log function \(y=\log_a(x)\) is the inverse of the exponential \(y=a^x\). Its graph passes through \((1,0)\), has a vertical asymptote at \(x=0\), and grows slowly when \(a>1\) (or falls slowly when \(00\). Range: all real numbers. Vertical asymptote at \(x=0\); the graph passes through \((1,0)\) for every base. If \(a>1\), the graph rises slowly; […]