2^n/32 = 4 => 2^n = 4 . 32 = 128 => n =7
27^n . 9^n = 9^27 . 81
=> (27.9)^n = 9^27 . 9^2
=> 243^n = 9^54
=> 243^n = 243^1458
vay n=1458
1/9 . 3^4 . 3^n+1 = 9^4
=> 9 . 3^n+1 = 6561
=> 3^n+1 = 6561 /9
=> 3^n+1 = 729
=> n = 5
\(a.\frac{2^n}{32}=4\Rightarrow2^n=32.4=128=2^7\Rightarrow n=7\)
\(b.27^{n^{ }}.9^n=9^{27}:81\Rightarrow3^{3n}.3^{2n}=3^{54}:3^4\)
\(\Rightarrow3^{5n}=3^{50}\Rightarrow n=50:5=10\)
\(c.\frac{1}{9}.3^4.3^{n+1}=9^4\Rightarrow\frac{1}{3^2}.3^4.3^{n+1}=3^8\)
\(\Rightarrow3^2.3^{n+1}=3^8\Rightarrow3^{n+1}=3^6\Rightarrow n=6-1=5\)
