$\frac{1}{5}$.$2^{x}$+$\frac{1}{3}$.$2^{x+1}$=$\frac{1}{5}$.$2^{7}$+ $\frac{1}{3}$. $2^{8}$
⇒ $2^{x}$.($\frac{1}{5}$+$\frac{1}{3}$.2) = $2^{7}$.$\frac{13}{15}$
⇒ $2^{x}$.$\frac{13}{15}$ = $2^{7}$.$\frac{13}{15}$
⇒ $2^{x}$ = $2^{7}$.$\frac{13}{15}$:$\frac{13}{15}$
⇒ $2^{x}$ = $2^{7}$
⇒ x = 7
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