a: \(\left(\dfrac{4}{5}\right)^{2x+7}=\dfrac{256}{625}\)
=>\(\left(\dfrac{4}{5}\right)^{2x+7}=\left(\dfrac{4}{5}\right)^4\)
=>2x+7=4
=>2x=-3
=>\(x=-\dfrac{3}{2}\)
b: \(\left(4x-3\right)^4=\left(4x-3\right)^2\)
\(\Leftrightarrow\left(4x-3\right)^4-\left(4x-3\right)^2=0\)
=>\(\left(4x-3\right)^2\left[\left(4x-3\right)^2-1\right]=0\)
=>\(\left(4x-3\right)^2\cdot\left(4x-3-1\right)\left(4x-3+1\right)=0\)
=>(4x-3)(4x-4)(4x-2)=0
=>\(\left[{}\begin{matrix}4x-3=0\\4x-4=0\\4x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=1\\x=\dfrac{1}{2}\end{matrix}\right.\)
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