1: =>3^x=81

=>x=4

2: =>2^x=8

=>x=3

3: =>x^3=2^3

=>x=2

4: =>x^20-x=0

=>x(x^19-1)=0

=>x=0 hoặc x=1

5: =>2^x=32

=>x=5

6: =>(2x+1)^3=9^3

=>2x+1=9

=>2x=8

=>x=4

7: =>x^3=115

=>\(x=\sqrt[3]{115}\)

8: =>(2x-15)^5-(2x-15)^3=0

=>(2x-15)^3*[(2x-15)^2-1]=0

=>2x-15=0 hoặc (2x-15)^2-1=0

=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1

=>x=15/2 hoặc x=8 hoặc x=7

1. Tìm số tự nhiên x biết:

1) \(3^x.3=243\)

\(3^x=243:3\)

\(3^x=81\)

\(3^x=3^4\)

\(\Rightarrow x=4\)

_____

2) \(7.2^x=56\)

\(2^x=56:7\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

_____

3) \(x^3=8\)

\(x^3=2^3\)

\(\Rightarrow x=3\)

_____

4) \(x^{20}=x\)

\(x^{20}-x=0\)

\(x\left(x^{19}-1\right)=0\)

\(\Rightarrow x=0\) hoặc \(x=1\)

5) \(2^x-15=17\)

\(2^x=17+15\)

\(2^x=32\)

\(2^x=2^5\)

\(\Rightarrow x=5\)

_____

6) \(\left(2x+1\right)^3=9.81\)

\(\left(2x+1\right)^3=729=9^3\)

\(\rightarrow2x+1=9\)

\(2x=9-1\)

\(2x=8\)

\(x=8:2\)

\(\Rightarrow x=4\)

_____

7) \(x^6:x^3=125\)

\(x^3=125\)

\(x^3=5^3\)

\(\Rightarrow x=5\)

_____

8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)

\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)

\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)

_____

9) \(3^{x+2}-5.3^x=36\)

\(3^x.\left(3^2-5\right)=36\)

\(3^x.\left(9-5\right)=36\)

\(3^x.4=36\)

\(3^x=36:4\)

\(3^x=9\)

\(3^x=3^2\)

\(\Rightarrow x=2\)

_____

10) \(7.4^{x-1}+4^{x+1}=23\)

\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)

\(4^{x-1}.\left(7+4^2\right)=23\)

\(4^{x-1}.\left(7+16\right)=23\)

\(4^{x-1}.23=23\)

\(4^{x-1}=23:23\)

\(4^{x-1}=1\)

\(4^{x-1}=4^1\)

\(\rightarrow x-1=0\)

\(x=0+1\)

\(\Rightarrow x=1\)

Chúc bạn học tốt

A) \(3^x\cdot3=243\)

\(\Leftrightarrow3^x=243:3=81\)

\(\Leftrightarrow3^x=3^4\)

\(\Leftrightarrow x=4\)

B) \(2^x-15=17\)

\(\Leftrightarrow2^x=17+15\)

\(\Leftrightarrow2^x=32\)

\(\Leftrightarrow2^x=2^5\)

\(\Leftrightarrow x=5\)

C) \(\left(x-1\right)^2-7=42\)

\(\Leftrightarrow\left(x-1\right)^2=49\)

\(\Rightarrow\orbr{\begin{cases}x-1=7\\x-1=-7\end{cases}\Rightarrow\orbr{\begin{cases}x=8\\x=-6\end{cases}}}\)

Câu a thì có nhiều cách nhưng mình chỉ làm 1 cách thôi nhé

a) 3^x . 3 = 243

=> 3^x . 3¹ = 3⁵

3^x = 3⁵ : 3¹

3^x = 3^5-1

3^x = 3⁴

<=> x = 4

b) 2^x - 15 = 17

2^x = 17 - 15

2^x = 2

<=> 2^x = 2¹ => x = 1

c) (x-1)² - 7 = 42

(x-1)² = 42 + 7

(x-1)² = 49

x-1 = 49 = 7.7

<=> x-1 = 7

x = 7 + 1

x = 8

ban tu lam di,luoi the

bai ki vay ,

a) \(2^x-15=17\)

\(2^x=17+15\)

\(2^x=32\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

b) \(27.3^x=243\)

\(3^x=243:27\)

\(3^x=9\)

\(\Rightarrow3^x=3^2\)

\(\Rightarrow x=2\)

c) \(3^x+25=26.2^2+2.3^0\)

\(3^x+25=104+2\)

\(3^x+25=106\)

\(3^x=106-25\)

\(3^x=81\)

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

\(\Rightarrow x=4\)

d) \(\left(7x-11\right)^3=2^5.5^2+200\)

\(\left(7x-11\right)^3=800+200\)

\(\left(7x-11\right)^3=1000\)

\(\Rightarrow\left(7x-11\right)^3=10^3\)

\(\Rightarrow7x-11=10\)

\(7x=10+11\)

\(7x=21\)

\(x=21:7\)

\(x=3\)

e) \(3^x.3=27\)

\(3^x=27:3\)

\(3^x=9\)

\(\Rightarrow3^x=3^2\)

\(\Rightarrow x=2\)

a) \(2^x-15=17\)

\(\Leftrightarrow2^x=17+15\)

\(\Leftrightarrow2^x=32\)

\(\Leftrightarrow2^x=2^5\)

\(\Leftrightarrow x=5\)

Vậy x = 5

b) \(27.3^x=243\)

\(\Leftrightarrow3^x=243:27\)

\(\Leftrightarrow3^x=9\)

\(\Leftrightarrow3^x=3^2\)

\(\Leftrightarrow x=2\)

Vậy x = 2

c) \(\left(7x-11\right)^3=2^5.5^2+200\)

\(\Leftrightarrow\left(7x-11\right)^3=800+200\)

\(\Leftrightarrow\left(7x-11\right)^3=1000\)

\(\Leftrightarrow\left(7x-11\right)^3=10^3\)

\(\Leftrightarrow7x-11=10\)

\(\Leftrightarrow7x=10+11\)

\(\Leftrightarrow7x=21\)

\(\Leftrightarrow x=21:7\)

\(\Leftrightarrow x=3\)

Vậy x = 3

d) \(3^x.3=27\)

\(\Leftrightarrow3^x=27:3\)

\(\Leftrightarrow3^x=9\)

\(\Leftrightarrow3^x=3^2\)

\(\Leftrightarrow x=2\)

Vậy x = 2

_Chúc bạn học tốt_

Giải:

\(a,2^x-15=17.\)

\(2^x=17+15.\)

\(2^x=32.\)

\(2^x=2^5.\)

\(\Rightarrow x=5\in N.\)

Vậy \(x=5.\)

\(b,\left(7x-11\right)^3=2^5.5^2+200.\)

\(\left(7x-11\right)^3=32.25+200.\)

\(\left(7x-11\right)^3=800+200.\)

\(\left(7x-11\right)^3=1000.\)

\(\left(7x-11\right)^3=10^3.\)

\(\Rightarrow7x-11=10.\)

\(\Rightarrow7x=10+11=21.\)

\(\Rightarrow x=21:7=3\in N.\)

Vậy \(x=3.\)

\(c,3^x+25=26.2^2+2.3^0.\)

\(3^x+25=26.2^2+2.1.\)

\(3^x+25=2\left(26.2+1\right).\)

\(3^x+25=2.53.\)

\(3^x+25=106.\)

\(3^x=106-25.\)

\(3^x=81.\)

\(3^x=3^4\Rightarrow x=4\in N.\)

Vậy \(x=4.\)

\(d,49.7^x=2041.\)(đề này sai).

Sửa đề:

\(49.7^x=2401.\)

\(7^x=2401:49.\)

\(7^x=49.\)

\(7^x=7^2\Rightarrow x=2\in N.\)

Vậy \(x=2.\)

\(e,3^x=243.\)

\(3^x=3^5\Rightarrow x=5\in N.\)

Vậy \(x=5.\)

~ Học tốt!!! ~

a, \(2^x-15=17\)

\(\Rightarrow2^x=32\Rightarrow2^x=2^5\)

Vì \(2\ne-1;2\ne0;2\ne1\) nên \(x=5\)

Vậy....

b, \(\left(7x-11\right)^3=2^5.5^2+200\)

\(\Rightarrow\left(7x-11\right)^3=32.25+200\)

\(\Rightarrow\left(7x-11\right)^3=1000=10^3\)

\(\Rightarrow7x-11=10\Rightarrow7x=21\Rightarrow x=3\)

Vậy.....

c, \(3^x+25=26.2^2+2.3^0\)

\(\Rightarrow3^x+25=26.4+2\)

\(\Rightarrow3^x=104+2-25\)

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

Vì \(3\ne-1;3\ne0;3\ne1\) nên x=4

Vậy.....

d,Sửa đề:\(49.7^x=2401\)

\(\Rightarrow7^2.7^x=7^4\Rightarrow7^{2+x}=7^4\)

Vì \(7\ne-1;7\ne0;7\ne1\) nên \(2+x=4\Rightarrow x=2\)

Vậy.....

Câu e làm tương tự! Chúc bạn học tốt!!!

1) \(2^x-15=17\)

\(2^x=17+15=32=2^5\)

\(\Rightarrow x=5\)

2) \(\left(7x-11\right)^3=2^5.5^2+200=32.25+200=1000=10^3\)

\(\Rightarrow7x-11=10\)

\(7x=11+10=21\)

\(x=3\)

3) \(3^x+25=26.2^2+2.3^0=26.4+2=106\)

\(3^x=106-25=81=3^4\)

\(\Rightarrow x=4\)

4) \(49.7^x=2041\)

\(7^2.7^x=7^4\)

\(\Rightarrow2+x=4\)

x = 2.

5) \(3^x=243=3^5\)

\(\Rightarrow x=5\)

 x²³:216=x¹⁵.x⁵

x²³: 6³= x²⁰

==> 6³=x²³:x²⁰

==> 6³=x³

==> x=6

(5^x.5^x+2):5³=125

==> 5^2x+2:5³=5³

==> 5^2x+2=5³.5³

==> 5^2x+2=5⁶

==> 2x+2=6

2x=6–2

2x=4

x=4:2

x=2

(3^x.3^x+4):3³=243

==> 3^2x+4:3³=3⁵

3^2x+4=3⁵.3³

3^2x+4=3⁸

==> 2x+4=8

2x=8–4

2x=4

x=4:2

x=2

3^x+3^x+1+3^x+2=243

3^x.1+3^x.3¹+3^x.3²=243

3^x.(1+3¹+3²)=243

3^x. (1+3+9)=243

3^x.13=243

3^x=243:13

3^x=...

1) Ta có: \(\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{7}{25}\cdot\dfrac{5}{7}\right)\)

\(=\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{1}{5}\right)\)

=0

2) Ta có: \(\dfrac{8}{17}\cdot\dfrac{4}{15}+\dfrac{8}{17}\cdot\dfrac{22}{15}-\dfrac{8}{15}\cdot\dfrac{9}{17}\)

\(=\dfrac{8}{17}\left(\dfrac{4}{15}+\dfrac{22}{15}-\dfrac{9}{15}\right)\)

\(=\dfrac{8}{17}\cdot\dfrac{15}{15}=\dfrac{8}{17}\)

3) Ta có: \(\dfrac{2021}{2}\cdot\dfrac{1}{3}+\dfrac{4042}{4}\cdot\dfrac{1}{5}+\dfrac{6063}{3}\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)+2021\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{8}{15}+\dfrac{2021}{2}\cdot\dfrac{44}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{52}{15}\)

\(=\dfrac{52546}{15}\)

4) Ta có: \(\dfrac{4}{7}\cdot\dfrac{2}{13}+\dfrac{8}{13}:\dfrac{7}{4}+\dfrac{4}{7}:\dfrac{13}{2}+\dfrac{4}{7}\cdot\dfrac{1}{13}\)

\(=\dfrac{4}{7}\left(\dfrac{2}{13}+\dfrac{8}{13}+\dfrac{2}{13}+\dfrac{1}{13}\right)\)

\(=\dfrac{4}{7}\)

1) Tính biểu thức:

1) PT \(\Leftrightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)

\(\Leftrightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}=\dfrac{x+36}{31}+\dfrac{x+36}{29}\)

\(\Leftrightarrow\left(x+36\right)\left(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}\right)=0\)

\(\Leftrightarrow x+36=0\) (Do \(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}>0\))

\(\Leftrightarrow x=-36\).

Vậy nghiệm của pt là x = -36.

2) x(x+1)(x+2)(x+3)= 24

⇔ x.(x+3)  .   (x+2).(x+1)  = 24

⇔(\(x^2\) + 3x) . (\(x^2\) + 3x + 2) = 24

Đặt \(x^2\)+ 3x = b

⇒ b . (b+2)= 24

Hay: \(b^2\) +2b = 24

⇔\(b^2\) + 2b + 1 = 25

⇔\(\left(b+1\right)^2\)= 25

+ Xét b+1 = 5 ⇒ b=4 ⇒  \(x^2\)+ 3x = 4 ⇒ \(x^2\)+4x-x-4=0 ⇒x(x+4)-(x+4)=0

⇒(x-1)(x+4)=0⇒x=1 và x=-4

+ Xét b+1 = -5 ⇒ b=-6 ⇒ \(x^2\)+3x=-6 ⇒\(x^2\) + 3x + 6=0

⇒\(x^2\) + 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))² = - \(\dfrac{15}{4}\)  Hay ( \(x^2\) +\(\dfrac{3}{2}\) )²= -\(\dfrac{15}{4}\) (vô lí)

⇒x= 1 và x= 4

1) -5 . x - ( - 3 )  = 13

-5 . x + 3 = 13

-5 . x = 13 - 3

-5 . x =10

x= 10 :  ( -5 )

x = -2

2) 3 . x  + 17 = 2

3 . x = 2 - 17

3 . x = -15

x = -15 : 3

x =  -5

3) (-5) . x =15

x = -3

4) 2x - (-17) = 15

2x + 17 = 15

2x = -2

x = -2 : 2

x= -1

5) -12 . ( x - 5 ) + 7 .(3-x) = 5

1=10

2=-5

3=-1

4=5

1) x - 2 = -6

x = -6 + 2

x = -4

2) -5 . x - ( -3 ) =13

-5 . x = 13 + ( -3 )

-5 . x = 10

x = 10 : ( -5 )

x = -2