a: \(\Leftrightarrow3^x\cdot\left(\dfrac{2}{3}\cdot3-7\right)=405\)

\(\Leftrightarrow3^x=-81\)(vô lý)

b: \(\left(0,4x-1,3\right)^2=5,29\)

=>0,4x-1,3=2,3 hoặc 0,4x-1,3=-2,3

=>0,4x=3,6 hoặc 0,4x=-1

=>x=9 hoặc x=-2,5

c: \(5\cdot2^{x+1}\cdot2^{-2}-2^x=284\)

\(\Leftrightarrow2^x\cdot5\cdot2\cdot2^{-2}-2^x=284\)

\(\Leftrightarrow2^x\cdot\left(\dfrac{5}{2}-1\right)=284\)

\(\Leftrightarrow2^x=\dfrac{568}{3}\)(vô lý)

d: \(\Leftrightarrow4^x\left(1+4^3\right)=4160\)

\(\Leftrightarrow4^x=64\)

hay x=3

\(\dfrac{2}{3}.3^{x+1}-7.3^x=-405\)

\(\Rightarrow\dfrac{2}{3}.3^x.3^1-7.3^x=-405\)

\(\Rightarrow2.3^x-7.3^x=-405\)

\(\Rightarrow3^x.\left(2-7\right)=-405\)

\(\Rightarrow3^x.-5=-405\)

\(\Rightarrow3^x=\dfrac{-405}{-5}\)

\(\Rightarrow3^x=81\)

Vì \(3^4=81\) nên \(x=4\)

\(\dfrac{2}{3}.3^{x+1}-7.3^x=-405\)

\(\Leftrightarrow\dfrac{2}{3}.3.3^x-7.3^x=-405\)

\(\Leftrightarrow3^x\left(2-7\right)=-405\)

\(\Leftrightarrow3^x.\left(-5\right)=-405\)

\(\Leftrightarrow3^x=81\)

\(\Leftrightarrow3^x=3^4\)

\(\Leftrightarrow x=4\)

Vậy..

a/ \(\frac{2}{3}.3^{x+1}-7.3^x=405\)

<=> 2.3^x-7.3^x=-405

<=> 5.3^x=405

<=> 3^x=81 = 3⁴

=> x=4

b/ (0,4x-1,3)²=5,29=(2,3)²

=> \(\hept{\begin{cases}0,4x-1,3=2,3\\0,4x-1,3=-2,3\end{cases}}\)=> \(\hept{\begin{cases}x=9\\x=-\frac{5}{2}\end{cases}}\)

c/ 5.2^x+1.2^-2-2^x=384

<=> 5.2^x-1-2.2^x-1=384

<=> 3.2^x-1=384

<=> 2^x-1=128=2⁷

=> x-1=7 => x=8

d/ 3^x+2.5^y=45^x

<=> 3^x+2.5^y=3^2x.5^x

=> \(\hept{\begin{cases}x+2=2x\\x=y\end{cases}}\)=> x=y=2

a) \(\frac{2}{3}.3^{x+1}-7.3^x=-405\)

=> \(\frac{2}{3}.3^x.3-7.3^x=-405\)

=> \(2.3^x-7.3^x=-405\)

=> \(3^x\left(2-7\right)=-405\)

=> \(3^x.\left(-5\right)=-405\)

=> \(3^x=-405:\left(-5\right)\)

=> \(3^x=81\)

=> \(x=4\)

b) \(\frac{3}{1-2x}=\frac{-5}{3x-2}\)

=> \(3\left(3x-2\right)=-5\left(1-2x\right)\)

=> \(9x-6=-5+10x\)

=> \(9x-10x=-5+6\)

=> \(-x=1\)

=> \(x=-1\)

tra mạng đi Min Cute