Hello,

I have problem with this equal, can you please explain me how on it?

x^logx - 100x = 0

I have problem with this equal

\(x^{\log_{10}(x)} - 100x = 0\)

I assume: \( \log(x) = \log_{10}(x)\)

\(\begin{array}{|rcll|} \hline x^{\log_{10}(x)} - 100x &=& 0 \\ x^{\log_{10}(x)} &=& 100x \quad | \quad \log_{10} \text{ both sides } \\ \log_{10}\left( x^{\log_{10}(x)} \right) &=& \log_{10}(100x) \\ \log_{10}(x)\log_{10}(x) &=& \log_{10}(100) + \log_{10}(x) \\ \log_{10}^2(x) &=& \log_{10}(10^2) + \log_{10}(x) \\ \log_{10}^2(x) &=& 2\log_{10}(10) + \log_{10}(x) \\ \log_{10}^2(x) &=& 2 + \log_{10}(x) \\ \log_{10}^2(x) - \log_{10}(x) - 2 &=& 0 \\\\ \log_{10}(x) &=& \dfrac{1 \pm \sqrt{1-4*(-2) } }{2} \\ \log_{10}(x) &=& \dfrac{1 \pm \sqrt{9} }{2} \\ \log_{10}(x) &=& \dfrac{1 \pm 3 }{2} \\ \hline \log_{10}(x) &=& \dfrac{1 + 3 }{2} \\ \log_{10}(x) &=& 2 \\ x &=& 10^2 \\ \mathbf{x} &=& \mathbf{100} \\ \hline \log_{10}(x) &=& \dfrac{1 - 3 }{2} \\ \log_{10}(x) &=& -1 \\ x &=& 10^{-1} \\ \mathbf{x} &=& \mathbf{0.1} \\ \hline \end{array}\)