\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(16.4^{x+1}-3.4^{x+1}=13.4^{11}\)

\(\left(16-3\right).4^{x+1}=13.4^{11}\)

\(13.4^{x+1}=13.4^{11}\)

\(\Rightarrow x+1=11\)

\(x=10\)

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

=> \(4^{x+1}.\left(4^2-3\right)=13.4^{11}\)

=> \(4^{x+1}.\left(16-3\right)=13.4^{11}\)

=> \(4^{x+1}.13=13.4^{11}\)

=> \(x+1=11\)

=> \(x=11-1=10\)

\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{14}=\frac{y}{21}\)

\(\frac{y}{7}=\frac{z}{4}\Rightarrow\frac{y}{21}=\frac{z}{12}\)

\(\Leftrightarrow\frac{x}{14}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{14+21-12}=\frac{69}{23}=3\)

\(\Rightarrow x=52;y=63;z=36\)

\(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{y}{7}=\frac{z}{4}\end{cases}\Rightarrow\hept{\begin{cases}\frac{x}{14}=\frac{y}{21}\\\frac{y}{21}=\frac{z}{12}\end{cases}\Rightarrow}\frac{x}{14}=\frac{y}{21}=\frac{z}{12}}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\frac{x}{14}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{14+21-12}=\frac{69}{23}=3\)

\(\Rightarrow\hept{\begin{cases}x=3.14=42\\y=3.21=63\\z=3.12=36\end{cases}}\)

(x - 2/3)³ = -1/27

=> (x - 2/3)³ = (-1/3)³

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

=> x = -1/3 + 2/3

=> x = 1/3

Từ bài ra ta có \(\left(x-\frac{2}{3}\right)^3=\left(\frac{-1}{3}\right)^3\)

\(\Rightarrow x-\frac{2}{3}=\frac{-1}{3}\)

\(\Rightarrow x=\frac{-1}{3}+\frac{2}{3}\)

\(\Rightarrow x=\frac{1}{3}\)

Vậy ... nếu đúng thì k nha

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}.5-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}.\left(5-3\right)-2.5^{11}=0\)

\(5^{x+3}.2-2.5^{11}=0\)

\(2\left(5^{x+3}-5^{11}\right)=0\)

\(\Rightarrow5^{x+3}-5^{11}=0\)

\(\Rightarrow5^{x+3}=5^{11}\)

\(\Rightarrow x+3=11\)

\(\Rightarrow x=8\)

vậy \(x=8\)

sai đề rồi bạn oi 5^x+4-3.5^x+3=0 mà sao mà bằng 2.5^11được

Lời giải:

1.

$3^{x+2}+4.3^{x+1}=7.3^6$

$3^{x+1}.3+4.3^{x+1}=7.3^6$

$3^{x+1}(3+4)=7.3^6$

$3^{x+1}.7=7.3^6$

$\Rightarrow 3^{x+1}=3^6$

$\Rightarrow x+1=6$

$\Rightarrow x=5$

2.

$5^{x+4}-3.5^{x+3}=2.5^{11}$

$5^{x+3}.5-3.5^{x+3}=2.5^{11}$

$5^{x+3}(5-3)=2.5^{11}$

$2.5^{x+3}=2.5^{11}$

$\Rightarrow 5^{x+3}=5^{11}$

$\Rightarrow x+3=11$

$\Rightarrow x=8$

3.

$4^{x+3}-3.4^{x+1}=13.4^{11}$

$4^{x+1}.4^2-3.4^{x+1}=13.4^{11}$

$4^{x+1}.16-3.4^{x+1}=13.4^{11}$

$13.4^{x+1}=13.4^{11}$

$\Rightarrow 4^{x+1}=4^{11}$

$\Rightarrow x+1=11$
$\Rightarrow x=10$

   2.3^x+2+4.3^x+1=10.3⁶

2.3.3^x+1+4.3^x+1=10.3⁶

   6.3^x+1+4.3^x+1=10.3⁶

            10.3^x+1=10.3⁶

=>3^x+1=3⁶

=>x+1=6 =>x=5

Ai thấy đúng cho mình nha!

\(2.3^{x+2}+4.3^{x+1}=10.3^6\)

\(2.3^{x+2}+2^2.3^{x+1}=2.5.3^6\)

\(2.3^{x+1}\left(3+2\right)=2.5.3^6\)

\(2.3^{x+1}.5=2.5.3^6\)

\(\Rightarrow x+1=6\Rightarrow x=5\)

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(\Rightarrow5^x.5^4-3.5^x.5^3=2.5^{11}\)

\(\Rightarrow5^x.5^3\left(5-3\right)=2.5^{11}\)

\(\Rightarrow5^x.2=2.5^8\)

\(\Rightarrow5^x=5^8\)

\(\Rightarrow x=8\)

Vậy \(x=8\)

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