A) \[x=1\]
B) \[x=2\]
C) \[x=3\]
D) \[x=4\]
Correct Answer: B
Solution :
[b] \[{{\log }_{3}}({{3}^{x}}-8)=2-x\Rightarrow {{3}^{x}}-8={{3}^{2-x}}\] where \[{{3}^{x}}-8>0\] \[\Rightarrow {{3}^{x}}-8=\frac{9}{{{3}^{x}}}\Rightarrow {{({{3}^{x}})}^{2}}-8({{3}^{x}})-9=0\] \[\Rightarrow ({{3}^{x}}+1)({{3}^{x}}-9)=0\Rightarrow {{3}^{x}}=9\,\,\,\,\,\,[\because \,\,\,{{3}^{x}}\ne -1]\] \[\therefore x=2\]
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