Tag Archives: Inequality

Exponential Inequalities using Logarithms

Exponential Inequalities using Logarithms

Inequalities are worked in exactly the same way except that there is a change of sign when dividing or multiplying both sides of the inequality by a negative number. \begin{array}{|c|c|c|} \hline \log_{2}{3}=1.6>0 & \log_{5}{3}=0.7>0 & \log_{10}{3}=0.5>0 \\ \hline \log_{2}{2}=1>0 & \log_{5}{2}=0.4>0 & \log_{10}{2}=0.3>0 \\ \hline \log_{2}{1}=0 & \log_{5}{1}=0 & \log_{10}{1}=0 \\ \hline \log_{2}{0.5}=-1<0 & \log_{5}{0.5}=-0.4<0 […]

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.$$\log_{10}{(x-2)}, \text{ then } x-2 \gt 0$$ […]