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

\(7\cdot4^x=112\)

\(\Rightarrow4^x=\dfrac{112}{7}\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

_____
\(2\cdot5^{x-3}=250\)

\(\Rightarrow5^{x-3}=\dfrac{250}{2}\)

\(\Rightarrow5^{x-3}=125\)

\(\Rightarrow5^{x-3}=5^3\)

\(\Rightarrow x-3=3\)

\(\Rightarrow x=3+3\)

\(\Rightarrow x=6\)

____

\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-\left(125+25\cdot7\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}+10\)

\(=12:\left[400:\left(500-300\right)\right]+10\)

\(=12:\left(400:200\right)+10\)

\(=12:2+10\)

\(=6+10\)

\(=16\)

\(7\cdot4^x=112\)

\(\Rightarrow4^x=112:7\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

Vậy \(x=2.\)

\(---\)

\(2\cdot5^{x-3}=250\)

\(\Rightarrow5^{x-3}=250:2\)

\(\Rightarrow5^{x-3}=125\)

\(\Rightarrow5^{x-3}=5^3\)

\(\Rightarrow x-3=3\)

\(\Rightarrow x=3+3\)

\(\Rightarrow x=6\)

Vậy \(x=6.\)

\(---\)

\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-300\right]\right\}+10\)

\(=12:\left\{400:200\right\}+10\)

\(=12:2+10\)

\(=6+10\)

\(=16\)

#\(Toru\)

x^3=125

x=5

x⁶:x³=125

x^6-3=125

x³=125

x³=5³

x=5

vậy x=5

a, \(\left(7.4^x+8.4^{x+1}\right).5=3120\)

\(7.4^x+8.4^x.4=3120:5\)

\(4^x\left(7+32\right)=624\)

\(4^x=624:39\)

\(4^x=16=4^2\)

\(\Rightarrow x=2\)

b, \(2018^2.2018^x=2018^6\)

\(2018^x=2018^6:2018^2=2018^4\)

\(\Rightarrow x=4\)

c, \(3^{x-2}-19=62\)

\(3^x:3^2=62+19\)

\(3^x=81.9=729=3^6\)

\(\Rightarrow x=6\)

d, \(5^{x+2}-5^{x+1}=2500\)

\(5^x\left(25-5\right)=2500\)

\(5^x=2500:20=125=5^3\)

\(\Rightarrow x=3\)

e, \(\left[\left(46-32\right)^2-\left(54-42\right)^2\right].2x-1872=0\)

\(\left[14^2-12^2\right].2x=1872\)

\(\left[196-144\right].2x=1872\)

\(52.2x=1872\)

\(2x=1872:52=36\)

\(\Rightarrow x=36:2=18\)

:)))

HỌC TỐT !

a) ( 7. 4^x + 8 . 4^x+1 ) . 5 = 3120

=> 7 . 4^x + 8 . 4^x . 4¹ = 624

=> 4^x ( 7 + 8 . 4 ) = 624

=> 4^x . 39 = 624

=> 4^x = 16

=> 4^x = 4²

=> x = 2

b) 2018² . 2018^x = 2018⁶

=> 2018^x = 2018⁴

=> x = 4

c) 3^x-2 - 19 = 62

=> 3^x-2 = 81

=> 3^x-2 = 3⁴

=> x - 2 = 4

=> x = 6

d) 5^x+2 - 5^x+1 = 2500

=> 5^x . 5² - 5^x . 5 = 2500

=> 5^x ( 5² - 5 ) = 2500

=> 5^x . 20 = 2500

=> 5^x = 125

=> 5^x = 5³

=> x = 3

e) [ ( 46 - 32 )² - ( 54 - 42 )² ] . 2x - 1872 = 0

=> [ 14²  - 12² ] . 2x = 1872

=> [ 196 - 144 ] . 2x = 1872

=> 52 . 2x = 1872

=> 2x = 36

=> x = 18

`#3107`

b)

`2.3^x = 162`

`\Rightarrow 3^x = 162 \div 2`

`\Rightarrow 3^x = 81`

`\Rightarrow 3^x = 3^4`

`\Rightarrow x = 4`

Vậy, `x = 4`

c)

`(2x - 15)^5 = (2 - 15)^3`

\(\Rightarrow \)`(2x - 15)^5 - (2x - 15)^3 = 0`

\(\Rightarrow \)`(2x - 15)^3 . [ (2x - 15)^2 - 1] = 0`

\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=15\\\left(2x-15\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x-15=1\\2x-15=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x=16\\2x=-14\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=-7\end{matrix}\right.\)

Vậy, `x \in`\(\left\{-7;8;\dfrac{15}{2}\right\}.\)

`d)`

\(3^{x+2}-5.3^x=?\) Bạn ghi tiếp đề nhé!

`e)`

\(7\cdot4^{x-1}+4^{x-1}=23?\)

\(4^{x-1}\cdot\left(7+1\right)=23\\ \Rightarrow4^{x-1}\cdot8=23\\ \Rightarrow4^{x-1}=\dfrac{23}{8}\)

Bạn xem lại đề!

`f)`

\(2\cdot2^{2x}+4^3\cdot4^x=1056\)

\(\Rightarrow2\cdot2^{2x}+\left(2^2\right)^3\cdot\left(2^2\right)^x=1056\\ \Rightarrow2\cdot2^{2x}+2^6\cdot2^{2x}=1056\\ \Rightarrow2^{2x}\cdot\left(2+2^6\right)=1056\\ \Rightarrow2^{2x}\cdot66=1056\\ \Rightarrow2^{2x}=1056\div66\\ \Rightarrow2^{2x}=16\\ \Rightarrow2^{2x}=2^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)

Vậy, `x = 2`

_____

\(10 -{[(x \div 3+17) \div 10+3.2^4] \div 10}=5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=10-5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=5\)

\(\Rightarrow\left(x\div3+17\right)\div10+48=50\)

\(\Rightarrow\left(x\div3+17\right)\div10=2\)

\(\Rightarrow x\div3+17=20\)

\(\Rightarrow x\div3=3\\ \Rightarrow x=9\)

Vậy, `x = 9.`

\(=>2\cdot4^x+64\cdot4^x=1056\)

\(=>4^x\cdot\left(2+64\right)=1056\)

\(=>4^x=1056:66=16\)

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

\(=>x=2\)

ti ck nha

2.2^2x + 4³.4^x = 1056

=> 2.4^x + 4³.4^x = 1056

=> (2 + 64).4^x = 1056

=> 66.4^x = 1056

=> 4^x = 1056 : 66

=> 4^x = 16

=> 4^x = 4²

=> x = 2

7.4^{x - 1} + 4^{x + 1} = 23

=> 7.4^x.1/4 + 4^x.4 = 23

=> (7/4 + 4).4^x = 23

=> 23/4.4^x = 23

=> 4^x = 23 : 23/4

=> 4^x = 4

=> x = 1

3^{x + 2} - 5.3^x = 36

=> 3^x.9 - 5.3^x = 36

=> 3^x.(9 - 5) = 36

=> 3^x.4 = 36

=> 3^x = 36 : 4

=> 3^x = 9 = 3²

=> 3^x = 2

2:

=>27:3^x=2*25-16-31=50-47=3

=>3^x=27/3=9

=>3^x=3^2

=>x=2

1:

b: \(=16\cdot55+16\cdot45-1\)

=16(55+45)-1

=1600-1

=1599

c: \(=\dfrac{1800}{49-\left[2\cdot\left(36-34\right)^3-5\right]}\)

\(=\dfrac{1800}{49-2\cdot2^3+5}=\dfrac{1800}{49-16+5}=\dfrac{1800}{38}\)=900/19

d: \(=\dfrac{5\cdot3^{11}\cdot2^{11}-3^{11}\cdot2^{11}}{2^{10}\cdot3^{10}\cdot2^2\cdot3+7\cdot2^{12}\cdot3^{12}}\)

\(=\dfrac{3^{11}\cdot2^{11}\left(5-1\right)}{2^{12}\cdot3^{11}\left(1+7\cdot3\right)}=\dfrac{1}{2}\cdot\dfrac{4}{1+21}=\dfrac{4}{22\cdot2}=\dfrac{1}{11}\)