\(9^{x+1}+5.3^{2x}=324\)

\(9^x.9+5.\left(3^2\right)^x=324\)

\(9^x.9+5.9^x=324\)

\(9^x.\left(5+9\right)=324\)

\(9^x.14=324\)

\(9^x=\frac{324}{14}\)

\(\Rightarrow x\in\varnothing\)

a) 5^{x + 1} - 2.5^x = 75

<=> 5^x.5 - 2.5^x = 75

<=> 5^x.3 = 75

<=> 5^x = 25

<=> 5^x = 5²

<=> x = 2

Vậy x = 2

b) 9^{x + 1} -  5.3^2x = 324

<=> (3²)^{x + 1} - 5.3^2x = 324

<=> 3^{2x + 2} - 5.3^2x = 324

<=> 3^2x.3² - 5.3^2x = 324

<=> 3^2x . 4 = 324

<=> 3^2x = 81

<=> 3^2x = 3⁴

<=> 2x = 4

<=> x = 2

Vậy x = 2

UIUYI

\(9^{x+1}-5.3^{2x}=324=>9^x.9-5.\left(3^2\right)^x=324=>\left(3^2\right)^x.9-5.\left(3^2\right)^x=324\)

\(=>3^{2x}.\left(9-5\right)=324=>3^{2x}=\frac{324}{4}=81=3^4=>2x=4=>x=2\)

vậy x=2

tick nhé

a) \(8\left(x-2\right)=3\)

\(\Leftrightarrow x-2=\dfrac{3}{8}\)

\(\Leftrightarrow x=\dfrac{3}{8}+2\)

\(\Leftrightarrow x=\dfrac{19}{8}\)

Vậy \(x=\dfrac{19}{8}\)

b) \(9^{x+1}-5.3^{2x}=324\)

\(\Rightarrow9^x.9-\left(3^2\right)^x.5=324\)

\(\Rightarrow9^x.9-9^x.5=324\)

\(\Rightarrow9^x\left(9-5\right)=324\)

\(\Rightarrow9^x.4=324\)

\(\Rightarrow9^x=\dfrac{324}{4}\)

\(\Rightarrow9^x=81\)

\(\Rightarrow9^x=9^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

a, \(8\left(x-2\right)=3\)

\(\Rightarrow x-2=\dfrac{3}{8}\Rightarrow x=\dfrac{19}{8}\)

b, \(9^{x+1}-5.3^{2x}=324\)

\(\Rightarrow9^x.9-5.9^x=324\)

\(\Rightarrow4.9^x=324\Rightarrow9^x=81=9^2\)

Vì \(9\ne\pm1;9\ne0\) nên \(x=2\)

Chúc bạn học tốt!!!

a) 8.(x-2)=3.

=> (x-2)= 3:8 = 0.375.

x = 0.375 + 2 = 2.375.

b) 9x+1 - 5.32x = 324.

<=> 9.9^x - 5.3^2x=324.

<=> 9.3^2x - 5.3^2x=324.

<=> 3^2x.(9-5)= 3^2x.4= 324.

<=> 3^2x=324:4=81=3⁴.

<=>2x = 4.

<=> x= 2.

Ta có :

9^{x + 1} - 5 . 3^2x = 324

(3²)^{x + 1} - 5 . 3^2x = 324

3^{2x + 2} - 5 . 3^2x = 324

9 . 3^2x - 5 . 3^2x = 324

3^2x (9 - 5) = 324

⇒ 3^2x = 324 : 4 = 81 ⇒ x = 2

b) 3.[5^2x+1 - (5²)^x] = 3.100

3( 5^2x+1-5^2x) = 3.100

-> 5^2x+1-5^2x = 100

mà 5³-5²= 100

-> 5^2x+1-5^2x = 5³-5²

^{Vậy x = 1}

c) (4²)^x : 4^x = 4²

<=>4^2x-x =4²

<=> 4^x = 4²

-> x=2

d) 2^x( 0,5 +4) = 72

2^x. 4,5 = 72

2^x = 72:4,5 = 16

2^x = 2⁴ = 16

-> x= 4