Question

Решите уравнения пжжжжж​

Answer 1

$\bf1)\displaystyle\bf2^x=3^x|:3^x\Rightarrow\frac{2^x}{3^x}=1\Rightarrow\bigg(\frac{2}{3}\bigg)^x=1\Rightarrow\bigg(\frac{2}{3}\bigg)^x=\bigg(\frac{2}{3}\bigg)^0\Longrightarrow\boxed{\bf x=0};\\2)25^x=7^{2x}|:7^{2x} \Rightarrow\frac{25^x}{7^{2x} }=1\Rightarrow\bigg(\frac{25}{49}\bigg)^x=1\Rightarrow\bigg(\frac{25}{49} \bigg)^x=\bigg(\frac{25}{49} \bigg)^0\Longrightarrow \boxed{\bf x=0} ;\\3)\bigg(\frac{1}{3} \bigg)^{2x} =8^x|:8^x\Rightarrow\dfrac{\Big(\dfrac13\Big)^{2x} }{8^x} }{} =1\Rightarrow$$\bf \displaystyle\Rightarrow \dfrac{\dfrac{1}{3^{2x} } }{8^x} =1\Rightarrow \frac{1}{3^{2x}\cdot8^x } =1\Rightarrow \frac{1}{9^x\cdot8^x} =1\Rightarrow \frac{1}{(9\cdot8)^x} =1\Rightarrow \frac{1}{72^x} =1|\cdot72^x\Rightarrow 1=72^x\Rightarrow 72^x=1\Rightarrow 72^x=72^0\Longrightarrow \boxed{\bf x=0} ;\\4)\bigg(\frac{1}{4} \bigg)^x=\bigg(\frac{1}{5} \bigg)^x|:(\frac{1}{5} )^x\Rightarrow \bigg(\dfrac{\dfrac{1}{4} }{\dfrac{1}{5} } \bigg)^x=1\Rightarrow \bigg(\frac{5}{4} \bigg)^x=1\Rightarrow$$\bf \displaystyle \bigg(\frac{5}{4} \bigg)^x=\bigg(\frac{5}{4} \bigg)^0\Longrightarrow \boxed{\bf x=0} .$