A) \[\frac{3}{2}\]
B) \[\frac{2}{3}\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
(a) \[{{\left( \frac{64}{125} \right)}^{2}}\times {{\left( \frac{4}{5} \right)}^{4}}\times {{\left( \frac{16}{25} \right)}^{2x+1}}={{\left( \frac{256}{625} \right)}^{3x}}\] Writing all expression in terms of \[\left( \frac{16}{25} \right)\]. \[={{\left( \frac{16}{25}\times \frac{4}{5} \right)}^{2}}\times {{\left( \frac{16}{25} \right)}^{2}}\times {{\left( \frac{16}{25} \right)}^{2x+1}}={{\left( \frac{16}{25} \right)}^{6x}}\] \[\Rightarrow {{\left( \frac{16}{25} \right)}^{2+1+2+2x+1}}={{\left( \frac{16}{25} \right)}^{6x}}\] \[\Rightarrow 2+1+2+2x+1=6x\] \[\Rightarrow 6+2=6x\] \[\Rightarrow 4x=6\] \[\Rightarrow x=3/2\].
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