A) 8
B) 10
C) 12.5
D) 6.5
Correct Answer: A
Solution :
Let \[{{3}^{3.5}}\times {{(3\times 7)}^{2}}\times {{(2\times 3\times 7)}^{2.5}}\times \frac{2}{{{2}^{2.5}}}\times {{7}^{3.5}}={{(21)}^{x}}\] Then, \[{{3}^{3.5}}\times {{3}^{2}}\times {{7}^{2}}\times {{2}^{2.5}}\times {{3}^{2.5}}\times {{7}^{2.5}}\times \frac{1}{{{2}^{2.5}}}\times {{7}^{3.5}}={{(21)}^{x}}\] \[\Rightarrow \] \[{{3}^{(3.5+2+2.5)}}\times {{7}^{(2+2.5+3.5)}}={{(21)}^{x}}\] \[\Rightarrow \] \[{{3}^{8}}\times {{7}^{8}}={{(21)}^{x}}\] \[\Rightarrow \] \[{{(21)}^{x}}={{(3\times 7)}^{8}}={{(21)}^{8}}\Rightarrow x=8\]
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