How to i solve this Exponential equation How to solve this exponential equation? 
$$7 \cdot 3^{x+1} - 5^{x+2}= 3^{x+4}- 5^{x+3}$$

Group them according to the base:
\begin{align}
&7\cdot 3^{x+1}-3^{x+4}=5^{x+2}-5^{x+3}\\
\implies&3^{x+1}(7-3^3)=5^{x+2}(1-5)\\
\implies&3^{x+1}\cdot (-20)=5^{x+2}\cdot(-4)\\
\implies&3^{x+1}\cdot 5=5^{x+2}\\
\implies&3^{x+1}=5^{x+1}
\end{align}
Generally, you would now use logarithms, although this case is rather obvious.
