d) \(3^x+3^{x+4}=738\)
\(3^x+3^x.3^4=738\)
\(3^x.\left(1+3^4\right)=738\)
\(3^x.82=738\)
\(3^x=9\)
\(3^x=3^2\)
\(\Rightarrow x=2\)
Vậy x=2
c) \(x^{20}-32x^{15}=0\)
\(\Leftrightarrow x^{15}.\left(x^5-32\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^{15}=0\\x^5-32=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x^5=32\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=0\\x=2\end{cases}}}\)
Vậy ...
\(4^{x-1}+5.4^{x-2}=576\)
\(\Leftrightarrow4^{x-1}+5.4^{x-1}.\frac{1}{4}=576\)
\(\Leftrightarrow4^{x-1}.\left(1+5.\frac{1}{4}\right)=576\)
\(\Leftrightarrow4^{x-1}.\frac{9}{4}=576\)
\(\Leftrightarrow4^{x-1}=256\)
\(\Leftrightarrow4^{x-1}=4^4\)
\(\Leftrightarrow x-1=4\)
\(\Leftrightarrow x=5\)
Vậy x=5
\(c,\text{ }x^{20}-32x^{15}=0\)
\(x^5\cdot x^{15}-32x^{15}=0\)
\(x^{15}\left(x^5-32\right)=0\)
\(\Rightarrow\text{ }\orbr{\begin{cases}x^{15}=0\\x^5-32=0\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x^5=32\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x^5=2^5\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
\(\Rightarrow\text{ }x\in\left\{0\text{ ; }2\right\}\)
c) \(x^{20}-32x^{15}=0\)
=> \(x^{15}.\left(x^5-32\right)=0\)
=> \(\orbr{\begin{cases}x^{15}=0\\x^5-32=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x^5=2^5\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
d) \(3^x+3^{x+4}=738\)
=> \(3^x.\left(1+3^4\right)=738\)
=> \(3^x.82=738\)
=> \(3^x=738:82\)
=> \(3^x=3^2\)
=> \(x=2\)
e) \(4^{x-1}+5.4^{x-2}=576\)
=> \(4^x.\frac{1}{4}+5.4^x.\frac{1}{16}=576\)
=> \(4^x.\left(\frac{1}{4}+\frac{5}{16}\right)=576\)
=> \(4^x.\frac{9}{16}=576\)
=> \(4^x=576:\frac{9}{16}\)
=> \(4^x=4^5\)
=> x = 5
