a) \(5^{3n+2}=25^{n+3}\)
\(\Leftrightarrow5^{3n+2}=5^{2\left(n+3\right)}\)
\(\Leftrightarrow3n+2=2\left(n+3\right)\)
\(\Leftrightarrow3n+2=2n+6\)
\(\Leftrightarrow n=4\)
b) \(6.5^{n-2}+10^2=2.5^3\left(n>1\right)\)
\(\Leftrightarrow6.5^{n-2}=2.5^3-10^2\)
\(\Leftrightarrow6.5^{n-2}=2.5^3-2^2.5^2\)
\(\Leftrightarrow6.5^{n-2}=2.5^2\left(5-2\right)\)
\(\Leftrightarrow6.5^{n-2}=2.5^2.3\)
\(\Leftrightarrow5^{n-2}=5^2\)
\(\Leftrightarrow n-2=2\)
\(\Leftrightarrow n=4\)
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