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

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

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

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

\(9^x.14=324\)

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

\(\Rightarrow x\in\varnothing\)

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

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

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!!!

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

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

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

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

\(\Rightarrow9^x=81\)

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

vậy x=2

\(\Rightarrow x=2\)

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

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

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

\(9^x.4=324\)

\(9^x=81=9^2\)

\(\Rightarrow x=2\)

Bài 4:

a: |x-2|=0

=>x-2=0

=>x=2

b: |x+3|=1

=>\(\left[\begin{array}{l}x+3=1\\ x+3=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1-3=-2\\ x=-1-3=-4\end{array}\right.\)

c: \(-3\left|4-x\right|=-9\)

=>|4-x|=3

=>|x-4|=3

=>\(\left[\begin{array}{l}x-4=3\\ x-4=-3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=7\\ x=1\end{array}\right.\)

d: |2x+1|=-2

mà -2<0<=|2x+1|

nên x∈∅

Bài 5:

a: \(\left(x+3\right)^2=36\)

=>\(\left[\begin{array}{l}x+3=6\\ x+3=-6\end{array}\right.\Rightarrow\left[\begin{array}{l}x=6-3=3\\ x=-6-3=-9\end{array}\right.\)

b: \(\left(x+5\right)^2=100\)

=>\(\left[\begin{array}{l}x+5=10\\ x+5=-10\end{array}\right.\Rightarrow\left[\begin{array}{l}x=10-5=5\\ x=-10-5=-15\end{array}\right.\)

c: \(\left(2x-4\right)^2=0\)

=>2x-4=0

=>2x=4

=>x=2

d: \(\left(x-1\right)^3=27\)

=>x-1=3

=>x=4

a) <=> (4x - 4x + 5)(4x + 4x - 5) = 15 <=> 40x = 15 <=> x = 3/8

Sorry, cái này mình nhầm

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