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\(a,\text{ }3^{x+4}-3^x=6480\)
\(3^x\left(3^4-1\right)=6480\)
\(3^x\cdot80=6480\)
\(3^x=6480\text{ : }80\)
\(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow\text{ }x=4\)
\(b,\text{ }x^5=4x^3\)
\(x^5-4x^3=0\)
\(x^3\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^3=0\\x^2-4=0\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x^2=4\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x=\pm2\end{cases}}\)
\(\Rightarrow\text{ }x\in\left\{0\text{ ; }-2\text{ ; }2\right\}\)
\(a,\text{ }3^{x+4}-3^x=6480\)
\(3^x\left(3^4-1\right)=6480\)
\(3^x\cdot80=6480\)
\(3^x=6480\text{ : }80\)
\(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow\text{ }x=4\)
\(b,\text{ }x^5=4x^3\)
\(x^5-4x^3=0\)
\(x^3\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^3=0\\x^2-4=0\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x^2=4\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x=\pm2\end{cases}}\)
\(\Rightarrow\text{ }x\in\left\{0\text{ ; }-2\text{ ; }2\right\}\)
