Question

Решить уравнение 3*9^х-1 - 5*3^х +12 = 0

Answer 1

$1)\; \; 3\cdot 9^{x-1}-5\cdot 3^{x}+12=0\\\\3\cdot 9^{x}\cdot 3^{-1}-5\cdot 3^{x}+12=0\quad \Big (\; 9^{x}=(3^2)^{x}=(3^{x})^2\; \Big )\\\\(3^{x})^2-5\cdot 3^{x}+12=0\\\\t=3^{x}>0\; ,\; \; \; t^2-5t+12=0\; , \\\\D=25-4\cdot 12=-23<0\; \; \Rightarrow \; \; \underline {x\in \varnothing }\\\\ili\\\\2)\; \; 3\cdot 9^{x-1}-5\cdot 3^{x+12}=0\\\\(3^{x})^2-5\cdot 3^{x}\cdot 3^{12}=0\\\\3^{x}\cdot (3^{x}-5\cdot 3^{12})=0\\\\a)\; \; 3^{x}=0\; \; \to \; \; x\in \varnothing \; ,\; t.k.\; \; 3^{x}>0\\\\b)\; \; 3^{x}=5\cdot 3^{12}\; \; \to \; \; \; x=log_3(5\cdot 3^{12})\; ,\; \; \underline {x=12+log_35}\\\\Otvet:\; \; x=12+log_35\; .$

Answer 2

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