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

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

\(16^x+7.4^x+5=3.2^x+2\)

<=> \(8.2^x+7.2.2^x+5=3.2^x+2\)

<=> \(8.2^x+7.2.2^x+5-3.2^x-2=0\)

<=> \(2^x\left(8+7.2-3\right)-3=0\)

<=> \(2^x.19=3\) 

<=> \(2^x=\frac{3}{19}\)

\(16^x=2^x.8^x\) mà

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/\(\Leftrightarrow\left(2^4\right)^x+7.\left(2^x\right)^2+5=3.2^x.4\)

Đặt \(2^x=y\) PT trở thành:

\(y^4+7y^2+5=12y\)

\(\Leftrightarrow y^4+7y^2-12y+5=0\)

Giải típ

\(7\cdot4^x=112\)

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

\(\Rightarrow4^x=16\)

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

\(\Rightarrow x=2\)

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

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

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

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

\(\Rightarrow x-3=3\)

\(\Rightarrow x=3+3\)

\(\Rightarrow x=6\)

____

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

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

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

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

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

\(=12:2+10\)

\(=6+10\)

\(=16\)

\(7\cdot4^x=112\)

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

\(\Rightarrow4^x=16\)

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

\(\Rightarrow x=2\)

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