Bài làm :

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

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

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

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

a/ 3^{4x + 4} = 81^{x + 3}

=> 81^{x + 4} = 81^{x + 3}

=> Đề sai!

b/ (2x - 1)⁵ = 81² : 9

=> (2x - 1)⁵ = 9³

Đề sai tiếp

Xem lại đi ==

Cô giáo tớ giao như thế!

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

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

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

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

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

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

\(x-140=-144\)

\(x=-4\)

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

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

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

\(\Rightarrow4x=3\)

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

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

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

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

           Bài làm :

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

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

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

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

Bài 1:

Tao có:

\(81^7mod\left(405\right)\)

\(81^3\equiv81mod\left(405\right)\)

\(81^6\equiv81^2\equiv81mod\left(405\right)\)

\(81^7\equiv81^2.81\equiv81mod\left(405\right)\)

Ta có:

\(27^9mod\left(405\right)\)

\(27^3\equiv243mod\left(405\right)\)

\(27^9\equiv243^3\equiv162mod\left(405\right)\)

Ta có:

\(9^{13}mod\left(405\right)\)

\(9\equiv9mod\left(405\right)\)

\(9^3\equiv324mod\left(405\right)\)

\(9^9\equiv324^3\equiv324mod\left(405\right)\)

\(9^{10}\equiv324.9\equiv81mod\left(405\right)\)

\(9^{13}\equiv81.324\equiv324mod\left(405\right)\)

\(81^7+27^9-9^{13}:405=81+162-324:405=-0,2\)

\(\Rightarrow81^7+27^9-9^{13}⋮405\left(đpcm\right)\)

Casio không biết có áp dụng ntn vào bài này được không nữa? Nhưng mình ôn hổm rày thấy có bài gần giống vậy, nên mình làm thử bạn tham khảo nha chúc bạn học tốt! ^^

\(27+\left(220-6x\right).3=615\)

\(\rightarrow\left(220-6x\right).3=615-27=588\)

\(\rightarrow220-6x=588:3=196\)

\(\rightarrow6x=220-196=24\)

\(\rightarrow x=24:6=4\)

\(315-\left(x-3\right).7=210\)

\(\Rightarrow\left(x-3\right).7=315-210=105\)

\(\Rightarrow x-3=105:7=15\)

\(\Rightarrow x=15+3=18\)

c) \(5^{x+2}+5^x=650\)

\(\Leftrightarrow 5^x(5^2+1)=650\)

\(\Leftrightarrow 5^x.26=650\)

\(\Rightarrow 5^x=25=5^2\Rightarrow x=2\)

d) \(81^x=(-3)^7\)

Ta thấy \(81^x>0, \forall x\in\mathbb{R}\)

\((-3)^7<0\)

Do đó pt đã cho vô nghiệm.

Lời giải:

a) \((2x-1)^3=(2x-1)^4\)

\(\Leftrightarrow (2x-1)^4-(2x-1)^3=0\)

\(\Leftrightarrow (2x-1)^3[(2x-1)-1]=0\)

\(\Leftrightarrow (2x-1)^3(2x-2)=0\)

\(\Rightarrow \left[\begin{matrix} 2x-1=0\\ 2x-2=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{1}{2}\\ x=1\end{matrix}\right.\)

b) \(2017^{x+2}=(2018-5^3)^{x+2}\)

\(\Rightarrow \left[\begin{matrix} x+2=0(1)\\ 2017=2018-5^3(2)\end{matrix}\right.\)

(1)\(\Rightarrow x=-2\)

(2): hiển nhiên vô lý

Vậy pt có nghiệm $x=-2$

Đề bài ??? 

a) \(\left(2x+1\right)^2=81\)

\(\Rightarrow\left(2x+1\right)^2=9^2\)

\(\Rightarrow2x+1=9\)

\(\Rightarrow2x=9-1=8\)

\(\Rightarrow x=8:2=4\)

\(\Rightarrow x=4\)

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

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

\(\Rightarrow3-x=1\)

\(\Rightarrow x=3-1=2\)

\(\Rightarrow x=2\)

c) \(\left(x+4\right)^3=125\)

\(\Rightarrow\left(x+4\right)^3=5^3\)

\(\Rightarrow x+4=5\)

\(\Rightarrow x=5-4=1\)

\(\Rightarrow x=1\)

k mk nha. CHÚC BẠN HỌC TỐT. ^_^