A) \[{{\log }_{5}}4\,\,and\,\,{{\log }_{5}}3\]
B) \[{{\log }_{3}}4\,\,and\,\,{{\log }_{4}}3\]
C) \[{{\log }_{3}}4\,\,and\,\,{{\log }_{3}}5\]
D) \[{{\log }_{5}}6\,\,and\,\,{{\log }_{5}}7\]
Correct Answer: A
Solution :
[a] \[{{\log }_{e}}5+{{\log }_{e}}\left( {{5}^{x}}-\frac{11}{5} \right)=2{{\log }_{e}}({{5}^{x}}-1)\] \[\Rightarrow \,\,{{5}^{x+1}}-11={{5}^{2x}}+1-2\times {{5}^{x}}\Rightarrow {{5}^{2x}}-{{7.5}^{x}}+12\] \[=0\] Let \[{{5}^{x}}=t,\] \[{{t}^{2}}-7t+12=0\,\,\,\,\Rightarrow \,\,\,t=4,3\] \[{{5}^{x}}=4,\] \[{{5}^{x}}=3\] \[\left. \begin{matrix} {{\log }_{5}}5x={{\log }_{5}}4 \\ x={{\log }_{5}}4 \\ \end{matrix} \right|\begin{matrix} {{\log }_{5}}{{5}^{x}}={{\log }_{5}}3 \\ x={{\log }_{5}}3 \\ \end{matrix}\]
You need to login to perform this action.
You will be redirected in
3 sec
