Решить уравнение. Ершова, С-25, вариант С-25.[tex] 3^{x-1}+ 3^{x}+ 3^{x+1} = 12^{x-1}+ 12^{x} [/tex]. Created by Russiagreat. algebra-ru

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Решить уравнение.
Ершова, С-25, вариант С-25.
[tex] 3^{x-1}+ 3^{x}+ 3^{x+1} = 12^{x-1}+ 12^{x} [/tex]

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$3^{x-1}+3^{x}+3^{x+1}=12^{x-1}+12^{x}\; |:3^{x}\ne 0\; (3^{x}\ \textgreater \ 0)\\\\ \frac{3^{x-1}}{3^{x}}+\frac{3^{x}}{3^{x}}+\frac{3^{x+1}}{3^{x}} = \frac{3^{x-1}\cdot 4^{x-1}}{3^{x}}+\frac{3^{x}\cdot 4^{x}}{3^{x}} \\\\3^{-1}+1+3=3^{-1}\cdot 4^{x-1}+4^{x}\\\\\frac{1}{3}+4=\frac{1}{3}\cdot 4^{x}\cdot \frac{1}{4}+4^{x}\\\\\frac{13}{3} =4^{x}\cdot (\frac{1}{12}+1)\\\\ \frac{13}{3} =4^{x}\cdot \frac{13}{12} \\\\4^{x}=\frac{13}{3}: \frac{13}{12} \\\\4^{x}= \frac{13}{3} \cdot \frac{12}{13} \\\\4^{x}=4\\\\x=1$

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