Question

Срочно, как вы разложите степень пятерки?(Фотка)​

Answer 1

5^{\frac{\lg \lg 3}{\lg 5}}-\lg 300

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$5^{\frac{\log _{10}\left(\log _{10}\left(3\right)\right)}{\log _{10}\left(5\right)}}-\log _{10}\left(300\right)=\\\bigg| \: \frac{\log _c\left(b\right)}{\log _c\left(a\right)}=\log _a\left(b\right)\\\\= 5^{\log _5\left(\log _{10}\left(3\right)\right)}-\log_{10}(300)=\\\bigg |\: a^{\log _a\left(b\right)}=b\\\\=\log _{10}\left(3\right)-\log _{10}\left(300\right) = \\\bigg | \: \log _c\left(a\right)-\log _c\left(b\right)=\log _c\left(\frac{a}{b}\right)$

$=\log _{10}\left(\frac{3}{300}\right)=\\= \log _{10}\left(\frac{1}{100}\right)=\\\bigg | \: \log _a\left(\frac{1}{x}\right)=-\log _a\left(x\right)\\\\=-\log _{10}\left(100\right) =\\=-\log _{10}\left(10^2\right)=\\=-2\log _{10}\left(10\right)=\\=-2\cdot \:1=\\=-2$

Ответ: −2.