1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)

2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)

\(2^x=2.2^8=2^9;x=9\)

4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)

\(\Leftrightarrow3^5.x=3^5.5;x=5\)

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

Ta có: \(7\cdot4^{x-1}+7\cdot4^{x+1}=23\)

\(\Leftrightarrow4^{x-1}\cdot\left(7+4^2\right)=23\)

\(\Leftrightarrow4^{x-1}\cdot23=23\)

\(\Leftrightarrow4^{x-1}=1\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

7.4^x-1 + 4^x+1 = 23

<=> 7.4^x-1 + 4^x-1.4² = 23

<=> 4^x-1( 7 + 4² ) = 23

<=> 4^x-1.23 = 23

<=> 4^x-1 = 1

<=> 4^x-1 = 4⁰

<=> x - 1 = 0

<=> x = 1

\(7.4^{x-1}+4^{x+1}=23\)

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

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

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

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

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

\(x-1=0\)

\(x=1\)

Đề đúng ko ad

1: \(5\cdot3^x=5\cdot3^4\)

nên \(3^x=3^4\)

hay x=4

2: \(7\cdot4^x=7\cdot4^3\)

nên \(4^x=4^3\)

hay x=3

3: \(8\cdot7^x=8\cdot7^6\)

nên \(7^x=7^6\)

hay x=6

: 

nên 

vậy x=4

2: 

nên 

vậy x=3

3: 

nên 

\(7.4^{x+1}-5.4^{x+1}=2048\)

\(\Rightarrow4^{x+1}.\left(7-5\right)=2048\)

\(\Rightarrow4^{x+1}.2=2048\)

\(\Rightarrow4^{x+1}=2048:2\)

\(\Rightarrow4^{x+1}=1024\)

\(\Rightarrow4^{x+1}=4^5\)

\(\Rightarrow x+1=5\)

\(\Rightarrow x=5-1\)

\(\Rightarrow x=4\)

Vậy \(x=4.\)

Chúc bạn học tốt!

x^3=125

x=5

x⁶:x³=125

x^6-3=125

x³=125

x³=5³

x=5

vậy x=5