A) \[{{\log }_{e}}\left( \frac{9}{\sqrt{8}} \right)\]
B) \[{{\log }_{9}}\left( \frac{9}{\sqrt{8}} \right)\]
C) \[{{\log }_{(9/2)}}\left( \frac{9}{\sqrt{8}} \right)\]
D) None of these
Correct Answer: C
Solution :
Given, equation is \[{{9}^{x}}-{{2}^{x+\frac{1}{2}}}={{2}^{x+\frac{3}{2}}}-{{3}^{2x-1}}\] \[\Rightarrow \] \[{{9}^{x}}-{{2}^{x}}.\sqrt{2}={{2}^{x}}\sqrt{8}-{{9}^{x}}{{.3}^{-1}}\] \[\Rightarrow \] \[{{9}^{x}}+\frac{{{9}^{x}}}{3}={{2.2}^{x}}\sqrt{2}+{{2}^{x}}\sqrt{2}\] \[\Rightarrow \] \[\frac{4}{3}{{9}^{x}}=3\sqrt{2}{{.2}^{x}}\] \[\Rightarrow \] \[{{\left( \frac{9}{2} \right)}^{x}}=\frac{9\sqrt{2}}{4}\] \[\Rightarrow \] \[{{\left( \frac{9}{2} \right)}^{x}}=\frac{9}{2\sqrt{2}}=\frac{9}{\sqrt{8}}\] \[\Rightarrow \] \[x={{\log }_{(9/2)}}\left( \frac{9}{\sqrt{8}} \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
