a) \(2^{x+1}+2^x=3.32\)
\(2^x\left(2+1\right)=3.32\)
\(2^x=32=2^5\)
\(x=5\)
b) \(5^{2x+1}-5^{2x}=100\)
\(5^{2x}\left(5-1\right)=4.25\)
\(5^{2x}=25=5^2\)
x=1
c) \(7^{3x+1}+7^{3x}=343.14^3\)
\(7^{3x}\left(7+1\right)=343.14^3\)
\(7^{3x}=\dfrac{7^3.14^3}{2^3}=7^3.7^3=7^6\)
\(3x=6\)
\(x=2\)