a, \(2^x:4=32\)
\(\Leftrightarrow2^x=128=2^7\Leftrightarrow x=7\)
b, \(5^{x+1}:5=5^4\)
\(\Leftrightarrow5^{x+1}=5^5\Leftrightarrow x+1=5\Leftrightarrow x=4\)
c, \(4^{2x-1}:4=16\)
\(\Leftrightarrow4^{2x-1}=64=4^3\Leftrightarrow2x-1=3\Leftrightarrow x=2\)
d, \(5.2^n+4.2^n=9.2^5\)
\(\Leftrightarrow2^n\left(5+4\right)=9.2^5\)
\(\Leftrightarrow2^n.9=9.2^5\)
\(\Leftrightarrow2^n=2^5\Leftrightarrow n=5\)
e, \(7.2^n+2^{n+1}=9.2^5\)
\(\Leftrightarrow7.2^n+2^n.2=9.2^5\)
\(\Leftrightarrow2^n\left(7+2\right)=9.2^5\)
\(\Leftrightarrow2^n.9=9.2^5\)
\(\Leftrightarrow2^n=2^5\Leftrightarrow n=5\)
f, \(3^x+3^{x+2}=270\)
\(\Leftrightarrow3^x+3^x.3^2=270\)
\(\Leftrightarrow3^x\left(1+9\right)=270\)
\(\Leftrightarrow3^x=27=3^3\Leftrightarrow x=3\)
