Question

СРОЧНО!! помогите!!!

Answer 1

Ответ:

2)x=18

3)x=3

4)x=-1

5)x∈(-∞;4]

Объяснение:

2) sqrt(x-2)=4  x>2

x-2=16

x=18

3) 3^(2x-3)=3^3

2x-3=3

2x=6

x=3

4) log(1/6) (3x+5)=log (1/6) (x+3)   x>-5/3

3x+5=x+3

2x=-2

x=-1

5) log(3) (1-2x)>=log(3) (9)   x<1/2

1-2x>=9

-2x>=8

x<=4

Answer 2

$2)\ \ \sqrt{x-2}-3=1\ \ , \ \ \ \ ODZ:\ x>2\\\\ \sqrt{x-2}=4\ \ ,\ \ \ x-2=16\ \ ,\ \ \underline {x=18}\\\\\\3)\ \ 3^{2x-3}=27\ \ \to \ \ \ 3^{2x-3}=3^3\ \ ,\ \ 2x-3=3\ \ ,\ \ 2x=6\ \ ,\ \ \underline {x=3}\\\\\\4)\ \ log_{1/6}(3x+5)=log_{1/6}(x+3)\ \ ,\\\\ODZ:\ \left\{\begin{array}{l}3x+5>0\\x+3>0\end{array}\right\ \ \left\{\begin{array}{ccc}x>-\frac{5}{3}\\x>-3\end{array}\right\ \ \to \ \ \ x>-\frac{5}{3}\\\\3x+5=x+3\\\\2x=-2\ \ ,\ \ \ x=-1\in ODZ\\\\Otvet:\ \ x=-1\ .$

$5)\ \ log_3(1-2x)\geq log_39\ \ ,\ \ \ ODZ:\ 1-2x>0\ \ ,\ \ x<\dfrac{1}{2}\\\\a=3>1\ \ \to \ \ 1-2x\geq 9\ \ ,\ \ -8\geq 2x\ \ ,\ \ 2x\leq -8\ \ ,\ \ x\leq -4\\\\Otvet:\ \ x\in (-\infty ;-4\, ]\ .$