334/MR00. zadatak / Matematika - Zbirka rešenih zadataka

MR-334 / 334. zadatak

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$\log_{10} (x^{2} + 19) - \log_{10} (x - 8) = 2$

\log_{10} (x^{2} + 19) - \log_{10} (x - 8) = 2

\log_{10} (x^{2} + 19) - \log_{10} (x - 8) = 2

\log_{10} (x^{2} + 19) - \log_{10} (x - 8) = l o g_{10} 10^{2}

l o g_{10} (x^{2} + 19) - l o g_{10} (x - 8) = \log_{10} 100

l o g_{10} \frac{x^{2} + 19}{x - 8} = \log_{10} 100

\frac{x^{2} + 19}{x - 8} = 100

x^{2} + 19 = 100 (x - 8)

x^{2} + 19 = 100 x - 800

x^{2} + 19 - 100 x + 800 = 0

x^{2} - 100 x + 819 = 0

x_{1, 2} = \frac{100 - \sqrt{10000 - 3276}}{2}

x_{1, 2} = \frac{100 \pm \sqrt{6724}}{2}

x_{1, 2} = \frac{100 \pm 82}{2}

x_{1} = 91 x_{2} = 9

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