\(a)\left(2^2\right)^x=2^5\)
\(\Leftrightarrow2^{2x}=2^5\)
\(\Leftrightarrow2x=5\)
\(\Leftrightarrow x=2,5\)
\(b)\left(3^x\right)^2=81\)
\(\Leftrightarrow3^{2x}=3^4\)
\(\Leftrightarrow2x=4\)
\(\Leftrightarrow x=2\)
\(c)8^{x+1}=2^{3003}\)
\(\Leftrightarrow\left(2^3\right)^{x+1}=2^{3003}\)
\(\Leftrightarrow2^{3\left(x+1\right)}=2^{3003}\)
\(\Leftrightarrow3\left(x+1\right)=3003\)
\(\Leftrightarrow x+1=1001\)
\(\Leftrightarrow x=1000\)
\(d)8^{x+1}=4^{1002}\)
\(\Leftrightarrow\left(2^3\right)^{x+1}=\left(2^2\right)^{1002}\)
\(\Leftrightarrow2^{3\left(x+1\right)}=2^{2004}\)
\(\Leftrightarrow3\left(x+1\right)=2004\)
\(\Leftrightarrow x+1=668\)
\(\Leftrightarrow x=667\)
