Tag Archives: Logarithm

Logarithmic Equations Reducible to Quadratics

Logarithmic Equations Reducible to Quadratics

Logarithmic Equations Reducible to Quadratic of Math Online Tutoring is based on the basic properties of logarithms such as;$$ \displaystyle\log_{a}{b} = \frac{1}{\log_{b}{a}} \\\log_{a}{b} = \frac{\log_{c}{b}}{\log_{c}{a}} \\$$ Question 1 Solve \(2 \log_{2}{x} – 9 \log_{x}{2} = 3 \). \( \begin{aligned} \displaystyle2 \log_{2}{x} – \frac{9}{\log_{2}{x}} &= 3 \\2 (\log_{2}{x})^2 – 9 &= 3 \log_{2}{x} \\2 (\log_{2}{x})^2 – […]

Logarithmic Inequalities

Logarithmic Inequalities

Solving logarithmic inequalities, it is important to understand the direction of the inequality changes if the base of the logarithms is less than 1.$$\log_{2}{x} \lt \log_{2}{y}, \text{ then } x \lt y \\\log_{0.5}{x} \lt \log_{0.5}{y}, \text{ then } x \gt y \\$$Also the domain of the logarithm is positive.$$\log_{10}{(x-2)}, \text{ then } x-2 \gt 0$$ […]