7 ∗ 3 x + 1 − 5 x + 2 = 3 x + 4 − 5 x + 3 {\displaystyle 7*3^{x+1}-5^{x+2}=3^{x+4}-5^{x+3}}
7 ∗ 3 x + 1 − 5 x + 2 = 3 x + 4 − 5 x + 3 21 ∗ 3 x − 25 ∗ 5 x = 3 x ∗ 81 − 5 x ∗ 125 21 ∗ 3 x − 3 x ∗ 81 − 25 ∗ 5 x + 5 x ∗ 125 3 x ( 21 − 81 ) + 5 x ( − 25 + 125 ) = 0 3 x ( − 60 ) + 5 x ∗ 100 = 0 − 60 + 5 x 3 x 100 = 0 t = 5 x 3 x − 60 + 100 t = 0 10 t = 6 t = 6 10 = 3 5 3 5 = 5 x 3 x 3 1 ∗ 5 − 1 = 5 x ∗ 3 − x x = − 1 x = − 1 {\displaystyle {\begin{aligned}7*3^{x+1}-5^{x+2}=3^{x+4}-5^{x+3}\\21*3^{x}-25*5^{x}=3^{x}*81-5^{x}*125\\21*3^{x}-3^{x}*81-25*5^{x}+5^{x}*125\\3^{x}(21-81)+5^{x}(-25+125)=0\\3^{x}(-60)+5^{x}*100=0\\-60+{\frac {5^{x}}{3^{x}}}100=0\\t={\frac {5^{x}}{3^{x}}}\\-60+100t=0\\10t=6\\t={\frac {6}{10}}={\frac {3}{5}}\\{\frac {3}{5}}={\frac {5^{x}}{3^{x}}}\\3^{1}*5^{-1}=5^{x}*3^{-x}\\x=-1\ \ \ \ \ \ x=-1\\\end{aligned}}}
