Lời giải:
$3^{2x}=27.3^x$

$\Rightarrow 3^{2x}=3^3.3^x=3^{3+x}$

$\Rightarrow 2x=3+x$

$\Rightarrow x=3$

27.3^x+2=3⁸

3³.3^x+2=3⁸

3^x+2+3=3⁸

3^x+5=3⁸

x+5=8

x=3

27.3^x+2=3⁸

       3^x+2=19683 : 27

     3^x+2= 729

       3^x+2=3\(^2\) \(^+\) \(^3\)

  => x= 3

27.3^x+2=3⁸

3³.3^x+2=3⁸

3^x+2=3⁸:3³

3^x+2=3⁵

x+2=5

x=5-2

x=3

               CHÚC BẠN HỌC TỐT!!!!

a: Ta có: \(2^{x-1}=32\)

\(\Leftrightarrow x-1=5\)

hay x=6

b: Ta có: \(3^{2x+1}=81\)

\(\Leftrightarrow2x+1=4\)

\(\Leftrightarrow2x=3\)

hay \(x=\dfrac{3}{2}\)

c: Ta có: \(2^x-26=6\)

\(\Leftrightarrow2^x=32\)

hay x=5

d: Ta có: \(27\cdot3^x=243\)

\(\Leftrightarrow3^x=9\)

hay x=2

`a) 27.3^x =243`

`3^x=243/27=9`

`3^x=3^2`

`=>x=2`

`b) 49.7^x =2401`

`7^x = 2401/49=49`

`7^x=7^2`

`=>x=2`

`c) 3^x +25 =26*2^2+2.3^0`

`3^x = 26.4+2.1-25 = 81`

`3^x =3^4`

`=>x=4`

\(e,27.3^x=243\\ \Leftrightarrow3^3.3^x=3^5\\ \Leftrightarrow3^{3+x}=3^5\\ \Rightarrow3+x=5\\ \Leftrightarrow x=2\\ g,49.7^x=2401\\ \Leftrightarrow7^2.7^x=7^4\\ \Leftrightarrow7^{2+x}=7^4\\ \Rightarrow2+x=4\\ \Leftrightarrow x=2\\ h,3^x+25=26.2^2+2.3^0\\ \Leftrightarrow3^x+25=26.4+2.1\\ \Leftrightarrow3^x=104+2-25\\ \Leftrightarrow3^x=81=3^4\\ Vậy:x=4\)

a,  2 x . 2 2 = 32

2 x + 2 = 2 5

x + 2 = 5

x = 3

Vậy x = 3

b,  27 . 3 x = 243

3 3 . 3 x = 3 5

3 3 + x = 3 5

x + 3 = 5

x = 2

Vậy x = 2

c,  2 x . 2 4 = 1024

2 x + 4 = 2 10

x + 4 = 10

x = 6

Vậy x = 6

d,  49 . 7 x = 2401

7 2 . 7 x = 7 4

7 2 + x = 7 4

2 + x = 4

x = 2

Vậy x = 2

a) \(2^x\cdot4=128\)

\(\Rightarrow2^x\cdot2^2=2^7\)

\(\Rightarrow2^{x+2}=2^7\)

\(\Rightarrow x+2=7\)

\(\Rightarrow x=5\)

b) \(\left(2x+1\right)^3=125\)

\(\Rightarrow\left(2x+1\right)^3=5^3\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=4:2\)

\(\Rightarrow x=2\)

c) \(2x-2^6=6\)

\(\Rightarrow2x-64=6\)

\(\Rightarrow2x=70\)

\(\Rightarrow x=70:2\)

\(\Rightarrow x=35\)

d) \(64\cdot4^x=45\)

\(\Rightarrow4^3\cdot4^x=45\)

\(\Rightarrow4^{x+3}=45\)

Xem lại đề

e) \(27\cdot3^x=243\)

\(\Rightarrow3^3\cdot3^x=3^5\)

\(\Rightarrow3^{x+3}=3^5\)

\(\Rightarrow x+3=5\)

\(\Rightarrow x=2\)

g) \(49\cdot7^x=2401\)

\(\Rightarrow7^2\cdot7^x=7^4\)

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

\(\Rightarrow x+2=4\)

\(\Rightarrow x=2\)

h) \(3^x=81\)

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

\(\Rightarrow x=4\)

k) \(3^4\cdot3^x=3^7\)

\(\Rightarrow3^{x+4}=3^7\)

\(\Rightarrow x+4=7\)

\(\Rightarrow x=3\)

n) \(3^x+25=26\cdot2^2+2\cdot3^0\)

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

\(\Rightarrow3^x+25=106\)

\(\Rightarrow3^x=81\)

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

\(x=4\)

`@` `\text {Ans}`

`\downarrow`

`a)`

`2^x*4 = 128`

`=> 2^x = 128 \div 4`

`=> 2^x = 2^7 \div 2^2`

`=> 2^x = 2^5`

`=> x = 5`

Vậy, `x = 5.`

`b)`

\(\left(2x+1\right)^3=125\)

`=> (2x + 1)^3 = 5^3`

`=> 2x + 1 = 5`

`=> 2x = 5-1`

`=> 2x = 4`

`=> x = 4 \div 2`

`=> x = 2`

Vậy, `x = 2`

`c)`

\(2x-2^6=6\)

`=> 2x = 6+2^6`

`=> 2x = 70`

`=> x = 70 \div 2`

`=> x = 35`

Vậy, `x = 35`

`d)`

\(64\cdot4^x=45\) Bạn xem lại đề

`e)`

`27*3^x = 243`

`=> 3^3 * 3^x = 3^5`

`=> 3^(3 + x) = 3^5`

`=> 3 + x = 5`

`=> x = 5 - 3`

`=> x = 2`

Vậy, `x = 2`

`g)`

`49* 7^x = 2401`

`=> 7^2 * 7^x = 7^4`

`=> 7^(2 + x) = 7^4`

`=> 2 + x = 4`

`=> x = 4 - 2`

`=> x = 2`

Vậy, `x = 2`

`h)`

`3^x = 81`

`=> 3^x = 3^4`

`=> x = 4`

Vậy, `x = 4`

`k)`

`3^4 * 3^x = 3^7`

`=> 3^(4 + x) = 3^7`

`=> 4 + x = 7`

`=> x = 7 - 4`

`=> x = 3`

Vậy, `x = 3`

`n)`

`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`

`=> 3^x = 3^4`

`=> x = 4`

Vậy, `x = 4.`

\(#48Cd\)