[toan] Mu va logarit

L

liverpool1

missneedlove said:
bai1....[TEX]5.4^x+2.25^x <= 7.10^x[/TEX]
bai2......[TEX]5^x-3^{x+1} > 2.(5^{x-1}-3^{x-2})[/TEX]
Bấm để xem đầy đủ nội dung ...

1) [TEX]5*{4}^{x}+2*{25}^{x} \leq 7*{10}^{x}[/TEX]
[TEX]=> 5*{2}^{2x}+2*{5}^{2x} -7*{10}^{x}\leq 0[/TEX]
[TEX]=> 5*{\frac{2}{5}}^{2x} -7*{\frac{2}{5}}^{x} +2\leq 0[/TEX]
[TEX]=> {\frac{2}{5}}^{x} =1 => x=0[/TEX]
hoặc [TEX]{\frac{2}{5}}^{x} =\frac{2}{5} => x=1[/TEX]

2) [TEX]{5}^{x} -3*{3}^{x} -\frac{2}{5}{5}^{x}+\fr=ac{2}{9}{3}^{x} >0[/TEX]
[TEX]=> \frac{3}{5} {5}^{x} -\frac{25}{9}{3}^{x} >0[/TEX]
[TEX]=> \frac{3}{5}{\frac{5}{3}}^{x} -\frac{25}{9} >0[/TEX]
[TEX]=> x =3[/TEX]
;)
 
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