a.
\(5^n+5^{n+2}=650\)
\(5^n\left(1+5^2\right)=650\)
\(5^n\left(1+25\right)=650\)
\(5^n\cdot26=650\)
\(5^n=650:26\)
\(5^n=25\)
\(5^n=5^2\Rightarrow n=2\)
b.
\(3^{n+3}+5\cdot3^n=864\)
\(3^n\left(3^3+5\right)=864\)
\(3^n\left(27+5\right)=864\)
\(3^n\cdot32=864\)
\(3^n=864:32\)
\(3^n=27\)
\(3^n=3^3\Rightarrow n=3\)
a) 5n + 5n+2 = 650
=> 5n + 5n . 52 = 650
=> 5n (1 + 52) = 650
=> 5n . 26 = 650
=> 5n = 25
=> n = 2
b) 3n+ 3 + 5.3n = 864
=> 3n . 33 + 5.3n = 864
=> 3n(33 + 5) = 864
=> 3n . 32 = 864
=> 3n = 27
=> n = 3
