Question

Алгебра 10 класс логарифмические уравнения 50 баллов

Answer 1

$1)x-1+log_{4}3=log_{4} (5^{x}-4^{x-1})\\\\log_{4}\frac{5^{x}-4^{x-1}}{3}=x-1\\\\\frac{5^{x}-4^{x-1}}{3}=4^{x-1}\\\\5^{x}-4^{x-1}=3*4^{x-1}\\\\5^{x}=4*4^{x-1}\\\\5^{x}=4*\frac{1}{4}*4^{x}\\\\5^{x}=4^{x}|:4^{x}\\\\(\frac{5}{4})^{x}=1\\\\(\frac{5}{4})^{x} =(\frac{5}{4})^{0}\\\\x=0$

$2)lglglog_{5}x=0\\\\lglog_{5}x=1\\\\log_{5}x=10\\\\x=5^{10}\\\\\sqrt[10]{x}=\sqrt[10]{5^{10} }=5$

$3)\frac{2lgx}{lg(5x-4)}=1\\\\x>0\\\\5x-4>0\\\\x>0,8\\\\lg(5x-4)\neq0\\\\5x-4\neq1\\\\x\neq1\\\\x\in(0,8;1)u(1;+\infty)\\\\2lgx=lg(5x-4)\\\\lgx^{2}=lg(5x-4)\\\\x^{2}=5x-4\\\\x^{2}-5x+4=0\\\\x_{1}=4\\\\x_{2} =1$

x = 1 - посторонний корень

Ответ : 4