\(2^x+2^{x+1}+2^{x+2}=56\)

\(2^x\left(1+2+2^2\right)=56\)

\(2^x\cdot7=56\)

\(2^x=8\)

\(x=3\)

a) Ta có 2^x + 2^{x + 1} + 2^{x + 2} = 56

⇒ 2^x ( 1 + 2¹ + 2² ) = 56

⇒ 2^x . 7 = 56

⇒ 2^x = 56 : 7 = 8 = 2³

Vậy x = 3

b) Ta có 3^x + 3^{x + 2} + 3^{x + 3} = 111

⇒ 3^x ( 1 + 3² + 3³ ) = 111

⇒ 3^x . 37 = 111

⇒ 3^x = 111 : 37 = 3 = 3¹

Vậy x = 1

a)  \(7x^2-16x=2x^3-56\)

\(\Leftrightarrow\)\(2x^3-7x^2+16x-56=0\)

\(\Leftrightarrow\)\(2x\left(x^2+8\right)-7\left(x^2+8\right)=0\)

\(\Leftrightarrow\)\(\left(2x-7\right)\left(x^2+8\right)=0\)

\(\Leftrightarrow\)\(2x-7=0\)

\(\Leftrightarrow\)\(x=3,5\)

Vậy...

b)  \(x^7+x^3+2x^5+2x=0\)

\(\Leftrightarrow\)\(x.\left(x^6+x^2+2x^4+2\right)=0\)

\(\Leftrightarrow\)\(x\left(x^2+2\right)\left(x^4+1\right)=0\)

\(\Leftrightarrow\)\(x=0\)

Vậy...

c)  \(\left(2x+1\right)x-5\left(x+\frac{1}{2}\right)=0\)

\(\Leftrightarrow\)\(2x\left(x+\frac{1}{2}\right)-5\left(x+\frac{1}{2}\right)=0\)

\(\Leftrightarrow\)\(\left(2x-5\right)\left(x+\frac{1}{2}\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-5=0\\x+\frac{1}{2}=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=2,5\\x=-0,5\end{cases}}\)

Vậy...

a: \(\Leftrightarrow2x^3-56-7x^2+16x=0\)

\(\Leftrightarrow2x\left(x^2+8\right)-7\left(x^2+8\right)=0\)

=>2x-7=0

hay x=7/2

b: \(\Leftrightarrow x^5\left(x^2+2\right)+x\left(x^2+2\right)=0\)

=>x(x²+2)(x⁴+1)=0

=>x=0

c: \(\Leftrightarrow2x^2+x-5x-\dfrac{5}{2}=0\)

\(\Leftrightarrow2x^2-4x-\dfrac{5}{2}=0\)

hay \(x\in\left\{\dfrac{5}{2};-\dfrac{1}{2}\right\}\)

1.

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{5}=\frac{y}{7}=\frac{z}{10}=\frac{2x}{10}=\frac{y}{7}=\frac{z}{10}$

$=\frac{2x+y-z}{10+7-10}=\frac{-21}{7}=-3$

$\Rightarrow x=-3.5=-15; y=-3.7=-21; z=-3.10=-30$

2.

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{3}=\frac{y}{4}=\frac{z}{6}=\frac{2x}{6}=\frac{4y}{16}=\frac{3z}{18}$

$=\frac{4y-2x+3z}{16-6+18}=\frac{-56}{28}=-2$

$\Rightarrow x=-2.3=-6; y=-2.4=-8; z=-2.6=-12$

a,  3 x + 1 : 3 4 = 81

3 x - 3 = 3 4

x – 3 = 4

x = 7

Vậy x = 7

b,  3 x + 3 . 3 x + 1 = 729

3 2 x + 4 = 3 6

2x + 4 = 6

x = 1

Vậy x = 1

c,  2 x + 3 . 2 x = 128

2 2 x + 3 = 2 7

2x + 3 = 7

x = 2

Vậy x = 2

d,  23 + 3 x = 5 6 : 5 3

23 + 3 x = 5 3

23 + 3x = 125

3x = 102

x = 34

Vậy x = 34

e,  2 x + 2 x + 4 = 272

2 x + 2 x . 2 4 = 272

2 x ( 1 + 2 4 ) = 272

2 x . 17 = 272

2 x = 16

2 x = 2 4

x = 4

Vậy x = 4