Question

Решить неравенство:
10^(3х+1) > 0,001
Решить неравенство:
Log6 (5x-2) > 3 log6 2 + 2
Найти производную функции:
Y = (1-4x)^9

Answer 1

$10^{3x+1} \ \textgreater \ 0.001 \\ 10^{3x+1} \ \textgreater \ 10^{-3} \\ 3x+1\ \textgreater \ -3 \\ 3x\ \textgreater \ -4 \\ x\ \textgreater \ -\frac{4}{3}$

$log_6 (5x-2) \ \textgreater \ 3log_6 2 + 2 \\ 5x-2\ \textgreater \ 0; x\ \textgreater \ 0.4 \\ log_6 (5x-2) \ \textgreater \ log_6 8 + log_6 36 \\ log_6 (5x-2) \ \textgreater \ log_6 288 \\ 5x-2 \ \textgreater \ 288 \\ 5x\ \textgreater \ 290 \\ x\ \textgreater \ 58$

$y=(1-4x)^9 \\ y'=9*(1-4x)^8*(-4)=-36(1-4x)^8$