Question

Решение уравнения...​

Answer 1

Ответ:

а) $log_{1/125}25$ = 0.2x+1

-2/3 = 0.2x+1

-5/3 = 1/5x

x = -25/3

x = -8 1/3

б) $log_{1/7} (2x+5)$ - $log_{1/7} 6$ = $log_{1/7} 2$

$log_{1/7} (1/3x+5/6)$ = $log_{1/7} 2$

1/3x+5/6 = 2

1/3x = 7/6

x = 21/6

x = 3 3/6

в) √(x² - 6) = √(-5x)

x² - 6 = -5x

x² + 5x - 6 = 0

(x+6)(x-1)=0

$x_{1} = -6$

$x_{2} = 1$

г) 2sin(x)+1 = 0

2sin(x) = -1

sin(x) = -1/2

x = arcsin(-1/2)

$x_{1}$ = -30°; $x_{2}$ = -150°

либо в радианах

$x_{1}$ = -pi/6; $x_{2}$ = -5pi/6