3^{4x - 1} : 3^x = 243

=> 3^{4x - 1 - x} = 3⁵

=> 3^{3x - 1} = 3⁵

=> 3x - 1 = 5

=> 3x = 6

=> x = 2

Vậy x = 2

\(3^{4x-1}:3^x=243\)

\(\Rightarrow3^{4x-1}:3^x=3^5\)

\(\Rightarrow4x-1=5\)

\(\Rightarrow4x=5+1\)

\(\Rightarrow4x=6\)

\(\Rightarrow x=\frac{3}{2}\)

\(3^{4x-1}:3^x=243\)

\(3^{4x-1-x}=243\)

\(3^{3x-1}=3^5\)

\(\Rightarrow3x-1=5\)

\(3x=6\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

ngũyn thị phươn uyn k hay = nguỹn phưn uyn >:

\(\left(15-4x\right)^5=243\)

\(\Rightarrow\left(15-4x\right)^5=3^5\)

=> 15 - 4x = 3

=> 4x = 12 => x = 3

Vậy x = 3

\(\left(3-x\right)^8=1^x\)

=> 3 - x = 1 => x = 2

3^4x-1:3x=243

⇔ 3^4x-1-x = 3⁵

⇔ 4x-1-x = 5

⇔ 3x-1 = 5

⇔ 3x = 6

⇔ x = 2

Chúc bạn học tốt ☺

1) PT \(\Leftrightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)

\(\Leftrightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}=\dfrac{x+36}{31}+\dfrac{x+36}{29}\)

\(\Leftrightarrow\left(x+36\right)\left(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}\right)=0\)

\(\Leftrightarrow x+36=0\) (Do \(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}>0\))

\(\Leftrightarrow x=-36\).

Vậy nghiệm của pt là x = -36.

2) x(x+1)(x+2)(x+3)= 24

⇔ x.(x+3)  .   (x+2).(x+1)  = 24

⇔(\(x^2\) + 3x) . (\(x^2\) + 3x + 2) = 24

Đặt \(x^2\)+ 3x = b

⇒ b . (b+2)= 24

Hay: \(b^2\) +2b = 24

⇔\(b^2\) + 2b + 1 = 25

⇔\(\left(b+1\right)^2\)= 25

+ Xét b+1 = 5 ⇒ b=4 ⇒  \(x^2\)+ 3x = 4 ⇒ \(x^2\)+4x-x-4=0 ⇒x(x+4)-(x+4)=0

⇒(x-1)(x+4)=0⇒x=1 và x=-4

+ Xét b+1 = -5 ⇒ b=-6 ⇒ \(x^2\)+3x=-6 ⇒\(x^2\) + 3x + 6=0

⇒\(x^2\) + 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))² = - \(\dfrac{15}{4}\)  Hay ( \(x^2\) +\(\dfrac{3}{2}\) )²= -\(\dfrac{15}{4}\) (vô lí)

⇒x= 1 và x= 4

a) \(4x=3y<=>\frac{x}{3}=\frac{y}{4}=>\frac{x}{15}=\frac{y}{20}\)

\(7y=5z<=>\frac{y}{5}=\frac{z}{7}=>\frac{y}{20}=\frac{z}{28}\)

Ap dung tinh chat bac cau ta duoc:

\(\frac{x}{15}=\frac{y}{20}=\frac{z}{28}=>\frac{2x}{30}=\frac{3y}{60}=\frac{z}{28}=\frac{2x+3y-z}{30+60-28}=\frac{186}{62}=3\)

=> x = 45  ;  y=60  ;  z=84

\(243-4x=3^9\div3^6\)

\(243-4x=3^3\)

\(243-4x=27\)

\(4x=243-27\)

\(4x=216\)

\(x=216\div4\)

\(x=54\)

\(5^x\div5^2=125\)

\(5^{x-2}=5^3\)

\(\Rightarrow x-2=3\)

\(\Leftrightarrow x=5\)

\(\left(x-30\right)\div2-150=10\)

\(\left(x-30\right)\div2=160\)

\(x-30=320\)

\(x=290\)

Thay \(y=1\) vào (1) ta được:

\(x=1+3\)

\(\Rightarrow x=4.\)

Vậy \(\left(x;y\right)=\left(4;1\right).\)

Chúc bạn học tốt!