Bài 9,

6²x73+36x3³=36x73+36x27=36(73+27)=36x100=3600.

197-\([\)6x(5-1)²+2022⁰\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.

Bài 10,

21-4x=13

=>4x=21-13=8

=>x=8:4=2.

30:(x-3)+1=4⁵:4³=4²=16

=>30:(x-3)=16-1=15

=>x-3=30:15=2

=>x=2+3=5.

(x-1)³+5x6=38

=>(x-1)³+30=38

=>(x-1)³=38-30=8=2³

=>x-1=2

=>x=3.

  Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

Bài 3

2\(^x\) = 16

2\(^x\) = 2⁴

  \(x=4\)

Vậy \(x=4\)

a) \(5\left(x+7\right)-10=2^3\cdot5\)

\(\Rightarrow5\left(x+7\right)-10=40\)

\(\Rightarrow5\left(x+7\right)=40+10\)

\(\Rightarrow x+7=\dfrac{50}{5}\)

\(\Rightarrow x+7=10\)

\(\Rightarrow x=10-7\)

\(\Rightarrow x=3\)

b) \(9x-2\cdot3^2=3^4\)

\(\Rightarrow9x-18=81\)

\(\Rightarrow9x=81+18\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=\dfrac{99}{9}\)

\(\Rightarrow x=11\)

c) \(5^{25}\cdot5^{x-1}=5^{25}\)

\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)

\(\Rightarrow5^{x-1}=1\)

\(\Rightarrow5^{x-1}=5^0\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

a) 5(�+7)−10=23⋅55(x+7)−10=23⋅5

$\Rightarrow 5\left(x+7\right)-10=40$

$\Rightarrow 5\left(x+7\right)=40+10$

⇒�+7=505⇒x+7=550​

$\Rightarrow x+7=10$

$\Rightarrow x=10-7$

$\Rightarrow x=3$

b) 9�−2⋅32=349x−2⋅32=34

$\Rightarrow 9x-18=81$

$\Rightarrow 9x=81+18$

$\Rightarrow 9x=99$

⇒�=999⇒x=999​

$\Rightarrow x=11$

c) 525⋅5�−1=525525⋅5x−1=525

⇒5�−1=525:525⇒5x−1=525:525

⇒5�−1=1⇒5x−1=1

⇒5�−1=50⇒5x−1=50

$\Rightarrow x-1=0$

$\Rightarrow x=1$

a: =>2x^3=58-4=54

=>x^3=27

=>x=3

b; =>(5-x)^5=2^5

=>5-x=2

=>x=3

c: =>(5x-6)^3=4^3

=>5x-6=4

=>5x=10

=>x=2

d: (3x)^3=(2x+1)^3

=>3x=2x+1

=>x=1

1=>2x³=54
=>x³=27  =>x=3
2=>(5-x)⁵=2⁵
=>5-x=2
=>x=3
3=>(5x-6)³=4³
=>5x-6=4
=>5x=10=>x=2
4=>3x=2x+1
=>x=1

a) \(5.3^x=405\)

\(\Rightarrow3^x=405:5\)

\(\Rightarrow3^x=81=3^4\)

\(\Rightarrow x=4\)

b) \(\left(x-2\right)^5=243\)

\(\Rightarrow\left(x-2\right)^5=3^5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=5\)

c) \(2^x+2^{x+4}=272\)

\(\Rightarrow2^x.\left(1+2^4\right)=272\)

\(\Rightarrow2^x.17=272\)

\(\Rightarrow2^x=272:17=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

d) Từ x + 1 đến x + 2 có số số hạng là: (30 - 1) : 1 + 1 = 30 (số)

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=795\)

\(\Rightarrow30x+\frac{\left(30+1\right).30}{2}=795\)

\(\Rightarrow30x+465=795\)

\(\Rightarrow30x=330\)

\(\Rightarrow x=330:30\)

\(\Rightarrow x=11\)

a) \(5.3^x=405\)

         \(3^x=\frac{405}{5}=81\)

          \(3^x=3^4\)

Vậy x = 4

b ) \(\left(x-2\right)^5=243\)

      \(\left(x-2\right)^5=3^5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=3+2=5\)

     Vậy x = 5

a, 5.3 ^x =405

3^x=405:5

3^x=81

=> x=4

b, (x-2)⁵=243

(x-2)⁵=3⁵

vì 5=5

nên x -2=3

<=> x=3+2

=>x=5

c, 2x  +   2x+4  =  272 

2^x+2^x+2⁴=272

2^x(1+2⁴)=272

2^x.17=272

2^x=272:17

2^x=16

vì 16=2⁴

=>x=4

d, (x+1)+(x+2)+(x+3)+.....+(x+30)=795

(x+x+x+..+x)+(1+2+3+..+30)=795

30x+456=795

30x=795-456

30x=330

x=330:30

x=11

vậy x=11

hc tốt

\(3^x+4^2=19^6:\left(19^3.19^2\right)-2.1^{2014}\)

\(\Rightarrow\) \(3^x+16=19^6:19^5-2\)

\(\Rightarrow\) \(3^x+16=19-2\)

\(\Rightarrow\) \(3^x+16=17\)

\(\Rightarrow\) \(3^x=1\)

\(\Rightarrow\) \(3^x=3^0\)

\(\Rightarrow\) \(x=0\)

\(a,\Rightarrow x=30-18=12\\ b,\Rightarrow x+6=45:5=9\\ \Rightarrow x=9-6=3\\ c,\Rightarrow38-3x=4^2=16\\ \Rightarrow3x=38-16=22\\ \Rightarrow x=\dfrac{22}{3}\)

Bài 6 :

a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)

c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)

d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

Bài 7 :

a) \(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Rightarrow10.3^x=3^{34}+3^{36}\)

\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)

\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)

b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)

\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)

\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)

c) Bài C bạn xem lại đề

d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

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