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

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

mình ko biết xin lỗi bn nha!

mình ko biết xin lỗi bn nha!

mình ko biết xin lỗi bn nha!

mình ko biết xin lỗi bn nha!

b)\(2^{x-1}+5\cdot2^{x-2}=\frac{7}{32}\)

\(2^x:2+5\cdot2^x:2^2=\frac{7}{32}\)

\(2^x:2+2^x:\frac{4}{5}=\frac{7}{32}\)

\(2^x\cdot\left(\frac{1}{2}+\frac{5}{4}\right)=\frac{7}{32}\)

\(2^x\cdot\frac{7}{4}=\frac{7}{32}\)

\(2^x=\frac{7}{32}:\frac{7}{4}=\frac{1}{8}\)

\(2^x=\frac{2^0}{2^3}=2^{-3}\)

\(\Rightarrow x=-3\)

a) \(4^x+4^{x+3}=4160\)

\(\Rightarrow4^x+4^x.4^3=4160\)

\(\Rightarrow4^x.\left(1+4^3\right)=4160\)

\(\Rightarrow4^x.65=4160\)

\(\Rightarrow4^x=64\)

\(\Rightarrow4^x=4^4\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

b) \(2^{x-1}+5.2^{x-2}=\frac{7}{32}\)

\(\Rightarrow2^x.\frac{1}{2}+5.2^x.\frac{1}{4}=\frac{7}{32}\)

\(\Rightarrow2^x.\left(\frac{1}{2}+5.\frac{1}{4}\right)=\frac{7}{32}\)

\(\Rightarrow2^x.\frac{7}{4}=\frac{7}{32}\)

\(\Rightarrow2^x=\frac{7}{32}:\frac{7}{4}\)

\(\Rightarrow2^x=\frac{1}{8}\)

\(\Rightarrow2^x=2^{-3}\)

\(\Rightarrow x=-3\)

Vậy \(x=-3\)

a)\(4^x+4^{x+3}=4160\)

\(4^x+4^x\cdot4^3=4160\)

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

\(4^x\cdot65=4160\)

\(4^x=4160:65=64\)

\(4^x=4^3\)

\(\Rightarrow x=3\)

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.

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

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

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

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

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

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