\(4,\\ a,\Rightarrow3^{x+1}=243=3^5\Rightarrow x+1=5\Rightarrow x=4\\ b,7\cdot2^x=56\Rightarrow2^x=8=2^3\Rightarrow x=3\\ c,x^3=8^2=64=4^3\Rightarrow x=4\\ d,x^{20}=x\Rightarrow x^{20}-x=0\Rightarrow x\left(x^{19}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^{19}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\\ e,2^x-15=17\Rightarrow2^x=32=2^5\Rightarrow x=5\\ f,\left(2x+1\right)^3=9\cdot81=9^3\\ \Rightarrow2x+1=9\Rightarrow x=4\\ g,2\cdot3^x=162\Rightarrow3^x=81=3^4\Rightarrow x=4\)
\(h,\left(3x-15\right)^5=\left(3x-15\right)^3\\ \Rightarrow\left(3x-15\right)^5-\left(3x-15\right)^3=0\\ \Rightarrow\left(3x-15\right)^3\left(9x^2-90x+225-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x-15=0\\9x^2-90x+224=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{16}{3}\\x=\dfrac{14}{3}\end{matrix}\right.\)
\(i,\Rightarrow x^3=125=5^3\Rightarrow x=5\)