Question

Как решать подобные примеры? ( 13 вариант )

Answer 1

$\ left ( {3over7} right )^{3-2x}=left ( {49over9} right )^{-3}\\ left ( {3over7} right )^{3-2x}=left ( ({3over7})^{-2} right )^{-3}\\ left ( {3over7} right )^{3-2x}=left ( {3over7} right )^{6}\\ 3-2x=6\ 2x=-3\ x=-1,5$

$\ left ( {51over9} right )^{71sqrt{x-1}-3}=left ( {9over51} right )^{3sqrt{x-1}-293}\\ left ( {9over51} right )^{-71sqrt{x-1}+3}=left ( {9over51} right )^{3sqrt{x-1}-293}\\ -71sqrt{x-1}+3=3sqrt{x-1}-293\ 74sqrt{x-1}=296\ sqrt{x-1}=4\ x-1=16\ x=17$

$\ 6*5^{-2x+3}-1=5^{-x+1}\ 6*5^3*5^{-2x}-1=5*5^{-x}\ t=5^{-x}(t>0)\ 5^3*6t^2-1=5t\ 5^3*6t^2-5t-1=0\ D+25+24*125=3025\ t_1={5+sqrt{3025}over 250*6}={1over25}\ t_1={5-sqrt{3025}over 250*6}=-{1over30}\\ 5^{-x}={1over25}, x=2\ 5^{-x}=-{1over30}, xinvarnothing$

Answer 2

Спасибо!