2:
a: 3x-15=30
=>3x=45
=>x=45/3=15
b: \(5x+5^2=2^4\cdot5\)
=>\(5x+25=16\cdot5=80\)
=>5x=55
=>x=11
c: \(2+x:5=6\)
=>x:5=4
=>x=4*5=20
d: \(3^x-1=26\)
=>\(3^x=26+1=27\)
=>x=3
5:
a: \(A=1+3+3^2+...+3^{101}\)
\(=\left(1+3+3^2\right)+3^3\left(1+3+3^2\right)+...+3^{99}\left(1+3+3^2\right)\)
\(=13\left(1+3^3+...+3^{99}\right)⋮13\)
b: n+4 chia hết cho n+1
=>\(n+1+3⋮n+1\)
=>\(3⋮n+1\)
=>\(n+1\in\left\{1;-1;3;-3\right\}\)
=>\(n\in\left\{0;-2;2;-4\right\}\)
mà n là số tự nhiên
nên \(n\in\left\{0;2\right\}\)