3.3².3³.3⁴......3^x=3¹⁹⁰

=>3^{(1+2+3+...........+x)}=3¹⁹⁰

=>1+2+3+.........+x=190

=>\(\frac{x.\left(x+1\right)}{2}\)=180

=>x.(x+1)=190.2

=>x.(x+1)=380

=>x=19

=\(\dfrac{7}{2}\)

\(3\cdot3^2\cdot3^3\cdot3^4\cdot....\cdot3^x=3^{190}\)

\(\Leftrightarrow3^{1+2+3+...+x}=3^{190}\)

\(\Leftrightarrow1+2+3+...+x=190\)

\(\Leftrightarrow\dfrac{x\left(x+1\right)}{2}=190\Leftrightarrow x\left(x+1\right)=380\)

\(\Leftrightarrow x^2+x-380=0\)

\(\Leftrightarrow x^2-19x+20x-380=0\)

\(\Leftrightarrow x\left(x-19\right)+20\left(x-19\right)=0\)

\(\Leftrightarrow\left(x-19\right)\left(x+20\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-19=0\\x+20=0\end{matrix}\right.\)\(\Leftrightarrow x=19\left(x>0\right)\)

dễ

3.3^2.3^3.............3^x=3^190

3^1+2+3+4+....+x=3^190

nên 1+2+3+.........+x=190

hay (x+1).x :2 =190        nen 190.2= (x+1) . x hay 380 =19.20

vay x=19

Đáp số Ra 19 đó các bạn ạ

dễ hình ephg là hình thoi

a) \(\dfrac{2^4\cdot5^2\cdot7}{2^3\cdot5\cdot7^2\cdot11}=\dfrac{2^3\cdot5\cdot10\cdot7}{2^3\cdot5\cdot7\cdot77}=\dfrac{10}{77}\)

\(\dfrac{2^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot2^4\cdot5^3\cdot14}=\dfrac{2^3\cdot3\cdot5^3\cdot7\cdot3^2\cdot8}{3\cdot2^3\cdot2\cdot5^3\cdot14}=\dfrac{7\cdot3^2\cdot8}{2\cdot14}=\dfrac{63\cdot8}{2\cdot14}=18=\dfrac{1386}{77}\)

rút gọn rồi quy đồng nha

2/3

\(=\dfrac{2}{3}\)

\(\dfrac{2^4.3^5}{2^3.3^6}=\dfrac{2.2^3.3^5}{2^3.3^5.3}=\dfrac{2}{3}\)

Ai tick mk lên 30 -> 40 điểm mk tick cho cả tháng 

2x - 2³. 3³ = 138

2x - 8 . 27  = 138

2x - 216     = 138

2x              = 138 + 216

2x              = 354

2x              = 354 : 2

 x               = 177

vậy x = 177

( 6x - 3⁴ ) . 7³    = 3 . 7⁴

( 6x - 81 ) . 343  = 3 . 2401

( 6x - 81 ) . 343  = 7203

  6x - 81            = 7203 : 343

  6x - 81            = 21

  6x                   = 21 + 81

  6x                   = 102

    x                   = 102 : 6

    x                   = 17

vậy x = 17