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nicoletad
Pe: 2013-11-02T23:31:28+02:00 In: In:

Sistem de ecuatii logaritmice

log a x + LOG a ^2 Y= 3/2 (log a x- logaritm in baza a din x);
log a^2 x+ log a y=5/2 (log a^2 x- logaritm in baza a patrat din x)
Acesta este un sistem. ajutati-ma sa-l rezolv!! Multumesc !

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2 raspunsuri

  1. PallMall

        \[ \begin{array}{l} \log _a x + \log _{a^2 } y = \frac{3}{2} \\ \log _{a^2 } x + \log _a y = \frac{5}{2} \\ \log _{a^2 } x = \frac{1}{{2\log _x a}} = \frac{1}{2}*\frac{{\log _x x}}{{\log _x a}} = \frac{1}{2}*\log _a x \\ \to \log _a x + \frac{1}{2}\log _a y = \frac{3}{2} \\ \to \frac{1}{2}\log _a x + \log _a y = \frac{5}{2}\,\,\,\,(inmultesc\,\,cu\,\, - \frac{1}{2}\,\,si\,\,adun) \\ \log _a x - \frac{1}{4}\log _a x = \frac{1}{4} \\ \to 3\log _a x = 1 \to \log _a x = \frac{1}{3} \to x = a^{\frac{1}{3}} \\ \to \log _a y = \3 - \frac{2}{3} \to \log _a y = \frac{7}{{3}} \to y = a^{\frac{7}{{3}}} \\ \end{array} \]

    nu am mai scris conditiile de existenta ale logaritmului , s-au subinteles … le pui tu ca sa fie corect

  2. nicoletad

    Va multumesc mult!

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