Chapter 6, Problem 34CR

To determine

To solve:the inequality

Answer to Problem 34CR

The solution of inequality is $=x>0.387$

Explanation of Solution

Given information The inequality is $6^x>12$

Formula used:

General laws of logarithm ${\log }_a\left(MN\right)={\log }_{a}M+{\log }_{a}N$

Calculation:

The solution of inequality is

Taking log with base 6 on both side

  $\begin{array}{l}{\log }_{6}6>{\log }_{6}12\\ x>{\log }_6\left(2\cdot 6\right)\\ x>{\log }_{6}2\cdot {\log }_{6}6\\ x>{\log }_{6}2\cdot 1\\ x>\frac{{\log }_{10}2}{{\log }_{10}6}\\ x>\frac{0.693}{1.792}\\ x>\frac{0.301}{0.778}\\ x>0.387\end{array}$

Hence, solution of inequality is $=x>0.387$