a: Ta có: \(\left(x-47\right)-115=0\)
\(\Leftrightarrow x-47=115\)
hay x=162
b: Ta có: \(\left(7x-11\right)^3=2^5\cdot5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=1000\)
\(\Leftrightarrow7x-11=10\)
\(\Leftrightarrow7x=21\)
hay x=3
c: Ta có: \(x^{10}=1^x\)
\(\Leftrightarrow x^{10}=1\)
hay \(x\in\left\{1;-1\right\}\)
d: Ta có: \(x^{10}=x\)
\(\Leftrightarrow x^{10}-x=0\)
\(\Leftrightarrow x\left(x^9-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
e: Ta có: \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Leftrightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Leftrightarrow\left(2x-15\right)^3\left(2x-15-1\right)\left(2x-15+1\right)=0\)
\(\Leftrightarrow\left(2x-15\right)^3\cdot\left(2x-16\right)\left(2x-14\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=7\end{matrix}\right.\)
g: Ta có: \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
\(\Leftrightarrow2\cdot3^x=3^{12}\cdot18=3^{14}\cdot2\)
Suy ra: \(3^x=3^{14}\)
hay x=14
