Ta có: \(5^{x-1}+3\cdot5^{x+1}=1900\)
\(\Leftrightarrow5^x:5+3\cdot5^x\cdot5=1900\)
\(\Leftrightarrow5^x\cdot\frac{1}{5}+15\cdot5^x=1900\)
\(\Leftrightarrow5^x\cdot\left(\frac{1}{5}+15\right)=1900\)
\(\Leftrightarrow5^x\cdot15,2=1900\)
\(\Leftrightarrow5^x=\frac{1900}{15,2}=125\)
\(\Leftrightarrow5^x=5^3\)
hay x=3
Vậy: x=3