4^x+3 - 3.4^x+1 = 13.4¹¹

4^x+1.(4² - 3) = 13.4¹¹

4^x+1.13 = 13.4¹¹

=> 4^x+1 = 4¹¹

=> x + 1 = 11

=> x = 10

4^x+3 - 3.4^x+1 = 13.4¹¹

4^x+1.(16-3) = 13.4¹¹

4^x+1.13 = 13.4¹¹

4^x+1 = 4¹¹

<=> x+1 = 11

x = 10

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.

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

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

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

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

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

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

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

\(\Leftrightarrow4^x.\left(4^3-3.4\right)=13.4^{11}\)

\(\Leftrightarrow4^x.52=13.4^{11}\)

\(\Leftrightarrow\frac{4^x.52}{13}=\frac{13.4^{11}}{13}\)

\(\Leftrightarrow4^x.4=4^{11}\)

\(\Leftrightarrow4^{x+1}=4^{11}\)

\(\Leftrightarrow x+1=11\)

\(\Leftrightarrow x=10\)

Vậy : \(x=10\)

4^x+3-3.4^x+1=13.4¹¹

4^x.4³-3.4^x.4=13.4¹¹

4^x(64-12)=13.4¹¹

4^x.52=13.4¹¹

4^x+1=4¹¹

x+1=11

x=10

\(\Leftrightarrow4^x\cdot64-4^x\cdot12=13\cdot4^{11}\)

\(\Leftrightarrow4^x=13\cdot\dfrac{4^{11}}{52}=4^{10}\)

=>x=10

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

\(\Rightarrow4^{x+1}.\left(4^2-3\right)=13.4^{11}\)

\(\Rightarrow4^{x+1}.\left(16-3\right)=13.4^{11}\)

\(\Rightarrow4^{x+1}.13=13.4^{11}\)

\(\Rightarrow x+1=11\)

\(\Rightarrow x=11-1\)

\(\Rightarrow x=10\)

\(\Rightarrow4^x\left(4^3-3.4\right)=13.4^{11}\)

\(\Rightarrow4^x.52=13.4^{11}\)

\(\Rightarrow4^x=4^{\left(-1\right)}.4^{11}\)

\(\Rightarrow4^x=4^{10}\)

=> x=10

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

\(\Leftrightarrow4^{x+1}.4^2-3.4^{x+1}=13.4^{11}\)

\(\Leftrightarrow4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(\Leftrightarrow4^{x+1}.13=13.4^{11}\)

\(\Leftrightarrow4^{x+1}=4^{11}\)

\(\Leftrightarrow x+1=11\)

\(\Leftrightarrow x=10\)

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

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

\(\Rightarrow4^{x+1}.13=13.4^{11}\)

\(\Rightarrow4^{x+1}=4^{11}\)

\(\Rightarrow x+1=11\)

\(\Rightarrow\text{x=10}\)

a) 

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

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

<=> \(4^{x+1}.13=13.4^{11}\)

<=> \(4^{x+1}=4^{11}\)

<=> \(x+1=11\)

<=> x=10

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

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

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

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

\(\Rightarrow x+1=11\)

\(x=10\)

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

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

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

=> \(4^{x+1}.13=13.4^{11}\)

=> \(x+1=11\)

=> \(x=11-1=10\)

\(4^{x+3}-3.4^{x+1}=13.4^{11}\Rightarrow4^{x+1}.4^2-3.4^{x+1}=13.4^{11}\Rightarrow4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(\Rightarrow4^{x+1}\left(16-3\right)=13.4^{11}\Rightarrow4^{x+1}.13=13.4^{11}\Rightarrow x+1=11\Rightarrow x=10\)

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

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

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

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

\(x+3=11\)

\(x=8\)

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

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

\(4^{x+1}.13=13.4^{11}\)

\(4^{x+1}=4^{11}\)

\(x+1=11\)

\(x=10\)