Question

\(a,3x+17x=340\)

\(b,\left|2x+1\right|=3\)

\(c,3^x+3^{x+1}+3^{x+2}=1053\)

Answer 1

\(a,3x+17x=340\)

\(x\left(17+3\right)=340\)

\(x20=340\)

\(x=340:20=17\)

\(b,\left|2x+1\right|=3\\ \Rightarrow\left[{}\begin{matrix}2x+1=3\\2x+1=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=3-1=2\\2x=-3-1=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)

\(c,3^x+3^{x+1}+3^{x+2}=1053\\ 3^x\left(1+3+9\right)=1053\\ 3^x.13=1053\\ 3^x=1053:13=81=3^4\\ \Rightarrow x=4\)