\(5^{x-1}.3+5^x=100\)
\(\Rightarrow5^{x-1}.3+5^{x-1}.5=1000\)
\(\Rightarrow5^{x-1}\left(3+5\right)=1000\)
\(\Rightarrow5^{x-1}.8=1000\)
\(\Rightarrow5^{x-1}=125\)
\(\Rightarrow5^{x-1}=5^3\)
\(\Rightarrow x-1=3\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
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\(5^{x-1}.3+5^x=1000\)
\(5^{x-1}.3+5^{x-1}.5=1000\)
\(5^{x-1}.\left(3+5\right)=1000\)
\(5^{x-1}.8=1000\)
\(5^{x-1}=\frac{1000}{8}\)
\(5^{x-1}=125\)
\(5^{x-1}=5^3\)
\(\rightarrow x-1=3\)
\(x=3+1\)
\(x=4\)
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