Cách kia hơi lằng nhằng.

Làm lại:

\(\left(-\frac{3}{4}\right)^{3x-1}=\frac{256}{81}=\left(-\frac{3}{4}\right)^{-4}\)

\(\Rightarrow3x-1=-4\)

\(\Rightarrow3x=-3\)

\(\Rightarrow x=-1\)

Ta có : \(\left(-\frac{3}{4}\right)^{-4}=\frac{256}{81}\)

do đó 3x - 1 = -4

=> 3x = -4 + 1 = -3

=> x = -3 : 3 = -1

\(\left(-\frac{3}{4}\right)^{3x-1}=\frac{256}{81}\Rightarrow\left(-\frac{3}{4}\right)^{3x}:\left(-\frac{3}{4}\right)=\frac{256}{81}\Rightarrow\left(-\frac{3}{4}\right)^{3x}=-\frac{64}{27}\Rightarrow\left(-\frac{3^3}{4^4}\right)^x=-\frac{64}{27}\Rightarrow\left(-\frac{27}{64}\right)^x=-\frac{64}{27}\Rightarrow x=-1\)

Bạn ơi , 3x - 1 là số mũ phải không . Gỉa sử vậy , ta có :

\(\frac{256}{81}=\frac{4^4}{\left(-3\right)^4}=\frac{1}{\frac{\left(-3\right)^4}{4^4}}=\frac{1}{\left(\frac{-3}{4}\right)^4}=\left(\frac{-3}{4}\right)^{-4}=\left(\frac{-3}{4}\right)^{3x-1}\)=> 3x - 1 = -4 => 3x = -4 + 1 = -3  

=> x = -3 : 3 = -1 

\(\left(\frac{-3}{4}\right)^{3x-1}=\left(\frac{4}{3}\right)^4=\left(\frac{1}{\frac{3}{4}}\right)^4\left[\left(\frac{3}{4}\right)^{-1}\right]^4=\left(\frac{3}{4}\right)^{-4}=\left(-\frac{3}{4}\right)^{-4}\) 

(Lũy thừa số mũ chẵn thì \(a^x\)= \(\left(-a\right)^x\))

\(\Rightarrow\)3m - 1 = -4 \(\Rightarrow\)3m = -3 \(\Rightarrow\)m = -1

\(\left(\frac{3}{4}\right)^{3x}=\frac{81}{256}\)

\(\left(\frac{3}{4}\right)^{3x}=\left(\frac{3}{4}\right)^4\)

\(3x=4\)

\(x=\frac{4}{3}\)

Chúc bạn học tốt ^^

\(\left(\frac{3}{4}\right)^{3x-1}=\frac{81}{256}\)

\(\left(\frac{3}{4}\right)^{3x-1}=\left(\frac{3^4}{4^4}\right)\)

\(\left(\frac{3}{4}\right)^{3x-1}=\left(\frac{3}{4}\right)^4\)

\(\Rightarrow3x-1=4\)

\(\Rightarrow3x=5\)

\(\Rightarrow x=\frac{5}{3}\)

phương an đề là :

\(\left(\frac{3}{4}\right)^{3x-1}=\frac{81}{256}\) mà 

\(\left(\frac{-3}{4}\right)^{3x-1}=\frac{256}{81}\)

\(\Rightarrow\left(\frac{-3}{4}\right)^{3x}:\left(\frac{-3}{4}\right)=\frac{256}{81}\)

\(\Rightarrow\left(\frac{-3}{4}\right)^{3x}=\frac{256}{81}.\left(\frac{-3}{4}\right)\)

\(\Rightarrow\left(\frac{-3}{4}\right)^{3x}=\frac{64}{27}\)

\(\Rightarrow\left(-\frac{3}{4}\right)^{3x}=\left(-\frac{4}{3}\right)^3\)

\(\Rightarrow1=\left(-\frac{4}{3}\right)^3.\left(-\frac{4}{3}\right)^{3x}\)

\(\Rightarrow1=\left(-\frac{4}{3}\right)^{-x}\)

\(\Rightarrow1=\left(-\frac{3x}{4}\right)\)

\(\Rightarrow1=-3x:4\)

\(\Rightarrow-3x=4\)

\(\Rightarrow x=-\frac{4}{3}\)

Ta có:

\(\frac{256}{81}=\frac{4^4}{"-3"^4}=\frac{1}{\frac{"-3"^4}{4}}=\frac{1}{"\frac{-3}{4}"^4}="\frac{-3}{4}"^4="\frac{-3}{4}"^{3x-1}\Rightarrow3x-1=-4\Rightarrow3x=-4+1\)

\(=-3\)

\(\Rightarrow x=-3:1=-1\)

tớ làm bừa đấy sai thì thôi nha

\(a,\left(1+3x\right)^4=256\)

\(\left(1+3x\right)^4=4^4\)

\(\Rightarrow\orbr{\begin{cases}1+3x=4\\1+3x=-4\end{cases}}\Rightarrow\orbr{\begin{cases}3x=3\\3x=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=\frac{-5}{3}\end{cases}}\)

\(b,720:\left(x-140\right)=3^3-2^3.4\)

\(720:\left(x-140\right)=-5\)

\(x-140=720:\left(-5\right)\)

\(x-140=-144\)

\(x=-4\)

\(c,16^x.4^3=512\)

\(\left(2^4\right)^x=8\)

\(2^{4x}=2^3\)

\(\Rightarrow4x=3\)

\(\Rightarrow x=\frac{3}{4}\)

\(d,\left(2x-1\right)^4=81\)

\(\left(2x-1\right)^4=3^4\)

\(\Rightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\Rightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)

           Bài làm :

\(1\text{)}...\Leftrightarrow\orbr{\begin{cases}\left(1+3x\right)^4=4^4\Leftrightarrow1+3x=4\Leftrightarrow3x=3\Leftrightarrow x=1\\\left(1+3x\right)^4=\left(-4\right)^4\Leftrightarrow1+3x=-4\Leftrightarrow3x=-5\Leftrightarrow x=-\frac{5}{3}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=1\\x=-\frac{5}{3}\end{cases}}\)

\(2\text{)}...\Leftrightarrow720\div\left(x-140\right)=-5\Leftrightarrow x-140=-144\Leftrightarrow x=-4\)

\(3\text{)}...\Leftrightarrow\left(2^4\right)^x.\left(2^2\right)^3=2^9\Leftrightarrow2^{4x}.2^6=2^9\Leftrightarrow2^{4x}=2^3\Leftrightarrow4x=3\Leftrightarrow x=\frac{3}{4}\)

\(4\text{)}...\Leftrightarrow\orbr{\begin{cases}\left(2x-1\right)^4=3^4\Leftrightarrow2x-1=3\Leftrightarrow2x=4\Leftrightarrow x=2\\\left(2x-1\right)^4=\left(-3\right)^4\Leftrightarrow2x-1=-3\Leftrightarrow2x=-2\Leftrightarrow x=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)

sai đề