1) 5^x(7 - 6) = 2·5^(-3) 5^x·2 = 2·5^(-3) 5^x = 5^(-3) x = -3 2) 6Cos2x +4SinxCosx=1 6( Cos^2 x- Sin^2 x) +4SinxCos x = Sin^2 x + Cos^2 x 6Co^2 x -6Sin^2 x +4SinxCosx -Sin^2 x - Cos^2 x =0 5Cos^2 x -5 Sin^2 x +4SinxCosx=0| :Cos^2 x≠0 5 - 5tg^2 x +4 tg x=0 tgx = z -5z^2 +4z +5 = 0 z = (-2+-√29)/-5. tg x = (-2+-√29)/-5 х = аrc tg(-2+-√29)/-5 +πk, где к∈Z
5^x·2 = 2·5^(-3)
5^x = 5^(-3)
x = -3
2) 6Cos2x +4SinxCosx=1
6( Cos^2 x- Sin^2 x) +4SinxCos x = Sin^2 x + Cos^2 x
6Co^2 x -6Sin^2 x +4SinxCosx -Sin^2 x - Cos^2 x =0
5Cos^2 x -5 Sin^2 x +4SinxCosx=0| :Cos^2 x≠0
5 - 5tg^2 x +4 tg x=0
tgx = z
-5z^2 +4z +5 = 0
z = (-2+-√29)/-5.
tg x = (-2+-√29)/-5
х = аrc tg(-2+-√29)/-5 +πk, где к∈Z