A) 2
B) 3
C) 1
D) no value of x
Correct Answer: A
Solution :
| \[\frac{{{8}^{x}}+{{27}^{x}}}{{{12}^{x}}+{{18}^{x}}}=\frac{7}{6}\] |
| \[\frac{{{(8)}^{x}}}{{{(12)}^{x}}}\frac{(1+{{(27/8)}^{x}})}{(1+{{(18/12)}^{x}})}=\frac{7}{6}\]\[\Rightarrow {{\left( \frac{2}{3} \right)}^{x}}\left( \frac{1+{{(3/2)}^{3x}}}{1+{{(3/2)}^{x}}} \right)=\frac{7}{6}\] |
| \[\therefore \]let \[{{\left( \frac{3}{2} \right)}^{x}}=t\] \[\Rightarrow \frac{1+{{t}^{3}}}{t\,(1+t)}=\frac{7}{6}\] \[\because \,\,\,t+1\ne 0\] |
| \[\frac{(1+t)({{t}^{2}}+1-t)}{t(1+t)}=\frac{7}{6}\]\[\Rightarrow \frac{{{t}^{2}}+1-t}{t}=\frac{7}{6}\]\[\Rightarrow t=\frac{2}{3}\,\,or\,\,\frac{3}{2}\] |
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