Question

Answer 1

\(a,\Rightarrow2\cdot3^{x-2}=49+113=162\\ \Rightarrow3^{x-2}=81=3^4\Rightarrow x-2=4\Rightarrow x-6\\ b,\Rightarrow2\left(5x-16\right)=9-1=8\\ \Rightarrow5x-16=4\Rightarrow x=4\\ c,\Rightarrow x^4-69=\dfrac{144}{12}=12\\ \Rightarrow x^4=81=3^4=\left(-3\right)^4\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\\ d,\Rightarrow x\left(x+1\right)=111222=333\cdot334\Rightarrow x=333\\ e,\Rightarrow\left(5x-2\right)^3=3^7:3^4=3^3\\ \Rightarrow5x-2=3\Rightarrow x=1\\ f,\Rightarrow\left(2-x\right)^{10x-10}=1\\ \Rightarrow2-x=1\Rightarrow x=1\)