ВЫРУЧАЙТЕ. БАЛЛЫ. ПОЖАЛУЙСТА.

Question 1

ВЫРУЧАЙТЕ.
БАЛЛЫ.
ПОЖАЛУЙСТА.

Question 2

Решите задачу:

$13^{log_{\frac{1}{13}}lgx^2}\ \textless \ (\frac{1}{10})^{lg\, log_{13}x^2}\; ,\; \; ODZ:\; \; x\in R\\\\13^{-log_{13}lgx^2}\ \textless \ 10^{-lg\, log_{13}x^2}\; \; \to \; \; \; 13^{log_{13}(lgx^2)^{-1}}\ \textless \ 10^{lg(log_{13}x^2)^{-1}}\\\\(lgx^2)^{-1}\ \textless \ (log_{13}x^2)^{-1}\; \; \to \; \; \; \frac{1}{lgx^2}\ \textless \ \frac{1}{log_{13}x^2}\\\\\frac{1}{lgx^2}-\frac{1}{log_{13}x^2}\ \textless \ 0\; \; \to \; \; \; \frac{log_{13}x^2-lgx^2}{lgx^2\cdot log_{13}x^2}\ \textless \ 0$

$\frac{log_{13}x^2-lgx^2}{lgx^2\cdot \frac{lgx^2}{lg13}} \ \textless \ 0\; \; \to \; \; \frac{lg13(log_{13}x^2-lgx^2)}{lg^2x^2}<0$

$Tak\; kak\; \; \frac{lg13}{lg^2x^2} \ \textgreater \ 0\; ,\; to\; \; log_{13}x^2-lgx^2\ \textgreater \ 0\; \; \Rightarrow \\\\ \frac{lgx^2}{lg13} -lgx^2\ \textgreater \ 0\; ,\; \; \frac{lgx^2-lg13\cdot lgx^2}{lg13}\ \textgreater \ 0\; ,\; \frac{lgx^2(1-lg13)}{lg13} \ \textgreater \ 0\; \Rightarrow \\\\Tak\; kak\; \; (1-lg13)=lg10-lg13\ \textless \ 0\; [\, lg10\ \textless \ lg13,t.k.\; 10\ \textless \ 13\, ],to\\\\ \frac{1-lg13}{lg13} \ \textless \ 0\; \; i\; \; lgx^2\ \textless \ 0\; \Rightarrow \; lgx^2\ \textless \ lg1\; \; \Rightarrow \; \; x^2\ \textless \ 1\\\\x^2-1\ \textless \ 0\; ,\; \; (x-1)(x+1)\ \textless \ 0\; \; \; \; +++(-1)---(1)+++\\\\x\in (-1,1)$