7^2+7^2x+2=2401

=>7^2+7^2x.7^2=2401

=>7^2.(1+7^2x)=2401

=>1+7^2x+1=49=7^2

=>....

\(\left(x-\frac{1}{2}\right)^2=0\)

\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=0^2\)

\(\Leftrightarrow x-\frac{1}{2}=0\)

\(\Leftrightarrow x=\frac{1}{2}\)

Vậy x = 1/2

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

\(\Leftrightarrow\left(x-2\right)^2=1^2\)

\(\Leftrightarrow x-2=1\)

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

Vậy x = 3 hoặc x = 1

\(\left(2x-1\right)^3=-8\)

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

\(\Leftrightarrow2x-1=-2\)

<=> 2x = -1

<=> x = -0,5

Vậy x = -0,5

\(\left(x-\frac{1}{2}\right)^2=0\)

\(x-\frac{1}{2}=0\)

\(x=\frac{1}{2}\)

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

\(\Leftrightarrow\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1+2\\x=-1+2\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)

Vậy\(x\in\left\{3;1\right\}\)
\(\left(2x-1\right)^3=-8\)

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

\(2x-1=-2\)

\(2x=\left(-2\right)+1\)

\(2x=-1\)

\(x=-1\times2\)

\(x=-2\)

\(x\left(\frac{1}{2}\right)^2=\frac{1}{16}\)

\(x\left(\frac{1}{2}\right)^2=\left(\frac{1}{4}\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x\frac{1}{2}=\frac{1}{4}\\x\frac{1}{2}=-\frac{1}{4}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{4}:\frac{1}{2}\\x=-\frac{1}{4}:\frac{1}{2}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{2}\end{cases}}}\)

\(49\times7^x=2401\)

   \(7^x=2401:49\)

\(7^x=49\)

\(7^x=7^2\)

\(\Rightarrow x=2\)

\(2x^x-15=17\)

\(2x^x=17+15\)

\(2x^x=32\)

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

\(\Rightarrow x\times x=5\)

\(\Rightarrow x^2=5\)

\(2^x+3\times2^x=32\)

\(2^x\times\left(3+1\right)=32\)

\(2^x\times4=32\)

\(2^x=32:4\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

\(2x\left(x-\frac{1}{7}\right)=0\)

\(x\left(x-\frac{1}{7}\right)=0:2\)

\(x\left(x-\frac{1}{7}\right)=0\)

\(x\times x-x\times\frac{1}{7}=0\)

\(x^2-x\frac{1}{7}=0\)

\(x-x=0:\frac{1}{7}\)

\(x-x=0\)

\(\Rightarrow x=0\)

a) \(64^x:16^x=256\)

\(\Rightarrow\left(2^6\right)^x:\left(2^4\right)^x=2^8\)

\(\Rightarrow2^{6x}:2^{4x}=2^8\)

\(\Rightarrow2^{6x-4x}=2^8\)

\(\Rightarrow2^{2x}=2^8\)

\(\Rightarrow2x=8\)

\(\Rightarrow x=4\)

b) \(\dfrac{-2401}{7^x}=-7\)

\(\Rightarrow\dfrac{-7^4}{7^x}=-7\)

\(\Rightarrow-7^{4-x}=-7\)

\(\Rightarrow7^{4-x}=7\)

\(\Rightarrow4-x=1\)

\(\Rightarrow x=4-1\)

\(\Rightarrow x=3\)

c) \(\dfrac{64}{\left(-4\right)^x}=-256\)

\(\Rightarrow\left(-4\right)^x=\dfrac{64}{-256}\)

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

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

\(\Rightarrow x=1\)

\(a) 64^x:16^x=256\\\Rightarrow (64:16)^x=256\\\Rightarrow 4^x=4^4\\\Rightarrow x=4\\---\)

\(b,\dfrac{-2401}{7^x}=-7\)

\(\Rightarrow7^x=-2401:\left(-7\right)\)

\(\Rightarrow7^x=343\)

\(\Rightarrow7^x=7^3\)

\(\Rightarrow x=3\)

\(c,\dfrac{64}{\left(-4\right)^x}=-256\)

\(\Rightarrow\left(-4\right)^x=64:\left(-256\right)\)

\(\Rightarrow\left(-4\right)^x=-\dfrac{1}{4}\)

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

\(\Rightarrow x=-1\)

#\(Toru\)

x=343

x=2187

x=ko bik

x=ko bik

\(a,2^x.4=128\\2^x.2^2=2^7\\ 2^x=\dfrac{2^7}{2^2}=2^{7-2}=2^5\\ Vậy:x=5\\ ----\\ b,\left(2x+1\right)^3=125=5^3\\ \Rightarrow 2x+1=5\\ 2x=5-1=4\\ x=\dfrac{4}{2}=2\\ ----\\ c,2x-2^6=6\\ 2x=6+2^6=6+64\\ 2x=70\\ x=\dfrac{70}{2}=35\\ ----\\ d,49.7^x=2401\\ 7^x=\dfrac{2401}{49}=49=7^2\\ Vậy:x=2\)

7^2 . 7^x = 7^4

7^x = 7^2

=> x= 2

49 . 7^X = 2401

<=> 7² . 7^X  = 7⁴

=> 7^X = 7⁴ : 7²

<=> 7^X = 7² => X= 2

\(7^x=\frac{2401}{49}\)

\(7^x=49\)

\(7^x=7^2\)

x = 2

49 . 7^x = 2401

=> 7² . 7^x = 7⁴

7^x = 7⁴ : 7²

7^x = 7²

=> x = 2

2) 25 : 5^x = 5^x

VD : 5^x : 5^x = 1

=> 25 : 5 = 5

=> 25 : 5¹ = 5¹

=> x = 1

1) 49 . 7^x = 2401

7^x = 2401 : 49

7^x = 49

=> 7^x = 7²

=> x = 2

Vậy x = 2

2) 25 : 5^x = 5^x

=> 5² = 5^x . 5^x

=> 5² = 5^{x + x}

=> 2 = x + x

=> 2 = 2x

=> x = 2 : 2

=> x = 1

Vậy x = 1

Chúc bạn học tốt!

\(a\))\(49.7^x\)\(=2401\)

\(\Rightarrow\) \(7^x\)\(=2401\div49\)

\(\Rightarrow\)\(7^x\) \(=49\)

\(\Leftrightarrow\) \(7^x\)\(=7^2\)

\(\Rightarrow\) \(x=2\)

\(b\)) \(25\div5^x\) \(=5^x\)

\(\Leftrightarrow5^2\) \(\div5^x\) \(=5^x\)

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

\(\Rightarrow\) \(2=x+x\)

\(\Leftrightarrow\) \(2=2x\)

\(\Rightarrow\) \(x=2\div2\)

\(\Rightarrow\) \(x=1\)