Matematyka
awiko10
2017-06-25 08:52:47
Rozwiaz- log(x^2+8) - log(2x) = Log3
Odpowiedź
wikciapyra22101999
2017-06-25 11:43:59

[latex]D={xin R:x^2+8 extgreater 0; 2x extgreater 0}=(0,infty)\ log(x^2+8)-log(2x)=log3\ logigg(dfrac{x^2+8}{2x}igg)=log3\ dfrac{x^2+8}{2x}=3\ x^2+8=6x\ x^2-6x+8=0\ x^2-2x-4x+8=0\ x(x-2)-4(x-2)=0\ (x-2)(x-4)=0\ xin{2,4}\ 2,4in D\\ oxed{Z_r={2,4}}\\Z_r-mathrm{zbi'or rozwiaza'n}[/latex]

ejastrzebska18
2017-06-25 11:45:14

[latex]log(x^2+8)-log(2x)=log3[/latex] [latex]x^2+8>0 qquad land qquad 2x>0[/latex] [latex]xinmathbb{R} qquad landqquad{x}>0[/latex] [latex]x>0[/latex] [latex]logleft(cfrac{x^2+8}{2x} ight)=log3[/latex] [latex]cfrac{x^2+8}{2x}=3[/latex] [latex]x^2+8=6x[/latex] [latex]x^2-6x+8=0[/latex] [latex]Delta = 36 - 32 = 4[/latex] [latex]x=cfrac{6-2}{2}=2 qquad lor qquad x=cfrac{6+2}{2}=4[/latex]

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