| The value of x is \[{{2}^{3}}({{5}^{0}}+{{3}^{2x}})=8\frac{8}{27}\]is |
A) \[\frac{3}{2}\]
B) \[\frac{2}{3}\]
C) \[-\frac{1}{3}\]
D) \[\frac{-\,\,3}{2}\]
Correct Answer: D
Solution :
| \[{{2}^{3}}\,\,({{5}^{0}}+{{3}^{2x}})=8\frac{8}{27}\]\[\Rightarrow \]\[8\,\,(1+{{3}^{2x}})=8+\frac{8}{27}\] |
| \[\Rightarrow \]\[(1+{{3}^{2x}})=1+\frac{1}{27}\] |
| \[\Rightarrow \]\[{{3}^{2x}}=\frac{1}{27}\]\[\Rightarrow \]\[{{3}^{2x}}={{3}^{-3}}\] |
| \[\Rightarrow \]\[2x=-\,\,3\]\[\Rightarrow \]\[x=-\,\,3/2\] |
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