`5n=125`

`=>n=125:5`

`=>n=25`

5ⁿ = 125

5ⁿ = 5³

n = 3

\(x^{50}=x\\ \Rightarrow x^{50}-x=0\\ \Rightarrow x\left(x^{49}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^{49}-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^{49}=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

`x^50=x`

`x^50-x=0`

`x(x^49-1)=0`

`=>x=0` hoặc `x^49-1=0`

`=>x=0` hoặc `x=1`

(8x-12):4.3³=3⁶

2x - 3 = 3⁶:3³

2x-3 = 3³

2x-3 = 27

2x = 27 + 3

2x = 30

x = 30:2

x=15

Vậy x thuộc {15}

chúc bạn làm bài tốt:D

\(\left(8x-12\right):4\cdot3^3=3^6\\ \Rightarrow\left(8x-16\right):4=3^6:3^3\\ \Rightarrow\left(8x-16\right):4=3^3\\ \Rightarrow8x-16=27\cdot4\\ \Rightarrow8x-16=108\\ \Rightarrow8x=108+16\\ \Rightarrow8x=124\\ \Rightarrow x=124:8\\ \Rightarrow x=\dfrac{131}{2}\)

5 nha bạn:D

Là sao 

3; 5; 7

1,2 và 3

\(4^{x+2}-4^x=240\\ 4^x\left(4^2-1\right)=240\\ 4^x\cdot15=240\\ 4^x=16\\ 4^x=4^2\\ x=2\)

4\(^{x+2}\) - 4\(^x\) = 240

4\(^x\). 4\(^2\) - 4\(^x\) . 1 = 240

4\(^x\). ( 16 - 1 ) = 240

4\(^x\). 15 = 240

4\(^x\) = 240 : 15

4\(^x\) = 16

Vậy x = 2

Lời giải:

Đặt $A=5+4^2+4^3+....+4^{49}$
$A=1+4+4^2+4^3+...+4^{49}$

$4A=4+4^2+4^3+....+4^{50}$

$\Rightarrow 4A-A=4^{50}-1$

$\Rightarrow 3A=4^{50}-1$

$\Rightarrow 4^{3x-1}-1=4^{50}-1$

$\Rightarrow 3x-1=50$

$\Rightarrow 3x=51$

$\Rightarrow x=17$

\(27^{n+1}\cdot9=3^{17}\)

\(3^{3^{n+1}}\cdot3^2=3^{17}\)

\(3^{3n+3+2}=3^{17}\)

\(3n+3+2=17\)

\(3n=12\)

\(n=4\)

27ⁿ⁺¹ . 9 = 3¹⁷

(3³)ⁿ⁺¹ . 3² = 3¹⁷

3³ⁿ⁺³ = 3¹⁷ : 3²

3³ⁿ⁺³ = 3¹⁵

3n + 3 = 15

3n = 15 - 3

3n = 12

n = 12 : 3

n = 4