1) \(\left(3^x-5\right)^4=2^8\)
\(\Leftrightarrow\left[{}\begin{matrix}3^x-5=4\\3^x-5=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3^x=9\\3^x=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3^x=3^3\\3^x=3^0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
Vậy \(x_1=0;x_2=3\)
b) \(3^{x+2}+3^x=10^2-10\)
\(\Leftrightarrow\left(3^2+1\right)\cdot3^x=100-10\)
\(\Leftrightarrow\left(9+1\right)\cdot3^x=90\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)
c) \(3^{x+1}-3^x=4\cdot5-2\)
\(\Leftrightarrow\left(3-1\right)\cdot3^x=20-2\)
\(\Leftrightarrow2\cdot3^x=18\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)
d) \(5^{x+2}-5^x=10^3:2+10^2\)
\(\Leftrightarrow\left(5^2-1\right)\cdot5^x=1000:2+100\)
\(\Leftrightarrow\left(25-1\right)\cdot5^x=500+100\)
\(\Leftrightarrow24\cdot5^x=600\)
\(\Leftrightarrow5^x=25\)
\(\Leftrightarrow5^x=5^2\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)
e) \(4^x+4^{x-1}=84:7\)
\(\Leftrightarrow\left(4+1\right)\cdot4^{x-1}=12\)
\(\Leftrightarrow5\cdot4^{x-1}=12\)
\(\Leftrightarrow4^{x-1}=\dfrac{12}{5}\)
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