\(5^{x-2}+5^{x+2}=3130\)
\(\Rightarrow5^x\cdot\dfrac{1}{25}+5^x\cdot25\)
\(\Rightarrow5^x\cdot\left(\dfrac{1}{25}+25\right)=3130\)
\(\Rightarrow5^x\cdot\dfrac{626}{25}=3130\)
\(\Rightarrow5^x=3130:\dfrac{626}{25}\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
Vậy: x=3
\(5^{x-2}+5^{x+2}=3130\\ \Leftrightarrow5^{-2}.5^x+5^2.5^x=3130\\ \Leftrightarrow5^x\left(\dfrac{1}{25}+25\right)=3130\\ \Leftrightarrow5^x.\dfrac{626}{25}=3130\\ \Leftrightarrow5^x=125\\ \Leftrightarrow5^x=5^3\\ \Leftrightarrow x=3\)
Vậy x = 3
\(5^{x-2}+5^{x+2}=3130\)
\(5^{x-2}+5^{x-2+4}=3130\)
\(5^{x-2}+5^{x-2}.5^4=3130\)
\(5^{x-2}.\left(1+5^4\right)=3130\)
\(5^{x-2}.626=3130\)
\(5^{x-2}=3130:626\)
\(5^{x-2}=5\)
\(x-2=1\)
\(x=1+2\)
\(x=3\)
