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a) \(5^{x-3}=125\)
\(\Rightarrow5^{x-3}=5^3\)
\(\Rightarrow x-3=3\)
\(\Rightarrow x=3+3\)
\(\Rightarrow x=6\)
b) \(x^{2012}:3=3^{2011}\)
\(\Rightarrow x^{2012}=3^{2011}\cdot3\)
\(\Rightarrow x^{2012}=3^{2011+1}\)
\(\Rightarrow x^{2012}=3^{2012}\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
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2012.(2011-x) + 25 = 55:53 = 25
2012.(2011-x) = 25 - 25 = 0
2011 - x = 0
x = 2011 - 0 = 2011
2012.(2011-x)+25=55:53
=>2012.(2011-x)+25=55-3
=>2012.(2011-x)+25=52
=>2012.(2011-x)+25=25
=>2012.(2011-x)=25-25
=>2012.(2011-x)=0
=>2011-x=0:2012
=>2011-x=0
=>x=0+2011
=>x=2011
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\(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right).x=\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{1}{2012}\)
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