Lanjutan 2 Contoh Soal Persiapan Semester Gasal 2019/2020 Kelas X Peminatan





\begin{array}{ll}\\ \fbox{23}.&\textrm{Diketahui persamaan}\\\\ &\displaystyle \frac{x^{2}}{10000}=\displaystyle \frac{1000}{x^{2\left ( {{^{10}\log x}} \right )-8}} \\\\ &\textrm{Hasil kali dari nilai-nilai}\: \: x\: \: \textrm{adalah}\: ....\\ &\begin{array}{lllllllll}\\ \textrm{A}.&10^{2}&&&\textrm{D}.&10^{7}\\ \textrm{B}.&10^{3}&\textrm{C}.&10^{4}&\textrm{E}.&10^{8} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{B}\\ &\begin{aligned}\displaystyle \frac{x^{2}}{10000}&=\displaystyle \frac{1000}{x^{2\left ( ^{10}\log x \right )-8}}\\ x^{2}.x^{2\left ( ^{10}\log x \right )-8}&=10^{3}.10^{4}\\ x^{2\left ( ^{10}\log x \right )-6}&=10^{7}\\ x^{2\log x-6}&=10^{7},\quad \textrm{di}-log-\textrm{kan masing-masing ruas}\\ \log x^{\log x^{2}-6}&= \log 10^{7}\\ \left ( 2\log x-6 \right )\log x&=7\\ 2\left ( \log x \right )^{2}-6\left ( \log x \right )-7&=0\\ \textrm{persamaan kuadrat yan}&\textrm{g variabelnya berupa}-log.\\ \textrm{Sehingga hasil kali dari}\, &\: \textrm{nilai-nilai}\: \: x-\textrm{nya adalah}:\\ \alpha +\beta &=-\displaystyle \frac{b}{a}\\ \log x_{1}+\log x_{2}&=-\displaystyle \frac{b}{a},\qquad \textrm{ingat bahwa}\: \: \log x=\, ^{10}\log x\\ \log x_{1}.x_{2}&=-\displaystyle \frac{-6}{2}\\ ^{10}\log x_{1}.x_{2}&=3\\ x_{1}.x_{2}&=10^{3} \end{aligned} \end{array}

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