A) \[3\times {{10}^{-3}}\]
B) \[27\times {{10}^{-3}}\]
C) \[9\times {{10}^{-3}}\]
D) 3000
Correct Answer: A
Solution :
(a) \[{{3}^{-x}}=3000\] \[\Rightarrow {{3}^{x}}={{\left( 3000 \right)}^{-1}}\] \[\Rightarrow {{\left( {{3}^{x}} \right)}^{2}}={{\left[ {{\left( 3000 \right)}^{-1}} \right]}^{2}}\] \[\Rightarrow {{3}^{2x}}={{\left( 3000 \right)}^{-1}}\] \[\Rightarrow {{3}^{2x+3}}={{\left( 3000 \right)}^{-1}}\times 9\] \[\Rightarrow {{10}^{3}}\times {{3}^{2x+3}}={{10}^{3}}\times {{\left( 3\times {{10}^{3}} \right)}^{-2}}\times 27\] \[={{10}^{3}}\times {{3}^{-2}}\times {{10}^{-6}}\times 27\] \[=3\times {{10}^{-3}}\].
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