# Logarithmic Differentiation

Share0 Share +10 Tweet0 Our Courses Basic Rule of Logarithmic Differentiation $$\displaystyle \dfrac{d}{dx}\log_e{x} = \dfrac{1}{x} \\ \dfrac{d}{dx}\log_e{f(x)} = \dfrac{f'(x)}{f(x)}$$ Practice Questions Question 1 Differentiate $y = \log_{e}(3x)$. \begin{aligned} \displaystyle \dfrac{d}{dx}\log_{e}(3x) &= \dfrac{(3x)’}{3x} \\ &= \dfrac{3}{3x} \\ &= \dfrac{1}{x} \end{aligned} Question 2 Differentiate $y = \log_{e}(2x-1)$. \( \begin{aligned} […]

# Logarithmic Inequalities

Share0 Share +10 Tweet0 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 […]

# 12 Patterns of Logarithmic Equations

Share0 Share +10 Tweet0 Solving logarithmic equations is done many ways using properties of logarithmic functions, such as multiply of logs, change the base and reciprocals of logarithms.  \begin{aligned} \displaystyle \large a^x = y \ &\large \Leftrightarrow x = \log_{a}{y} \\ \large \log{a} + \log{b} &= \large \log{(a \times b)} \\ \large \log{a} – […]