Question

Решите неравенство (1/2)^(3x-7)>0,04.

Answer 1

$( frac{1}{2} )^{3x-7} textgreater 0,04\\2^{7-3x} textgreater frac{4}{100} \\2^{7-3x} textgreater frac{1}{25}\\2^{7-3x} textgreater 5^{-2}\\2^{7-3x} textgreater 2^{log_25^{-2}}\\7-3x textgreater log_25^{-2}\\7-3x textgreater -2cdot log_25\\3x textless 7+2cdot log_25\\x textless frac{7}{3}+frac{2}{3}cdot log_25$