a) \(2^{x+1}-2^x=32\)

\(\Rightarrow2^x\left(2-1\right)=2^5\)

\(\Rightarrow2^x.1=2^5\)

\(\Rightarrow x=5\)

b) \(2^{x+1}=2\)

\(\Rightarrow2^{x+1}=2^1\)

\(\Rightarrow x+1=1\)

\(\Rightarrow x=0\)

\(2^{x+1}-2^x=32\)

\(2^x.2-2^x=32\)

\(2^x\left(2-1\right)=32\)

\(2^x=32\)

\(x=5\)

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

1. 2^x=16\(\Rightarrow\)X=4

2. 2^2x-1=2⁷

\(\Rightarrow\)2⁷=2^2.4-1

Vậy x =4

x=4 nha chị

\(2^x+2^{x+2}=32.\left(2^2+1\right)\)

\(\Rightarrow2^x+2^{x+2}=32.5\)

\(\Rightarrow2^x+2^{x+2}=160\)

\(\Rightarrow2^x\left(1+4\right)=160\)

\(\Rightarrow2^x.5=160\)

\(\Rightarrow2^x=160:5=32\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

Vậy x = 5

Các bạn giúp mk nha gấp lắm luôn đó nha🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗

TL:

a.\(2^6.2^n=2^{11}\) 

 \(2^{6+n}=2^{11}\) 

\(\Rightarrow n=5\) 

b. \(3^7:3^n=3^4\) 

  \(3^{7-n}=3^4\) 

\(\Rightarrow n=3\) 

c.\(2^n.32=2^{10}\)

 \(2^{n+5}=2^{10}\) 

\(\Rightarrow n=5\) 

\(\left(X-1\right)^2=16\)

   \(\left(X-1\right)^2=4^2\)

      X  -1    =4

       X=5

\(2^{X-1}=32\)

\(2^{X-1}=2^{6-1}\)

X=6

H NHA

a.\(x-1^2=16\)                                                           b.\(2^{x-1}=32\)                                     

\(\Leftrightarrow x-1=16\)                                                      \(\Leftrightarrow2^{x-1}=2^5\)

\(\Leftrightarrow x=16-1\)                                                      \(\Leftrightarrow x-1=5\)

\(\Leftrightarrow x=15\)                                                               \(\Leftrightarrow x=5+1\)

Vậy x = 15                                                                        \(\Leftrightarrow x=6\) 

                                                                                             Vậy x= 6

Cho mk xin 1 tk nhé!

Ta có : ( x - 1 )² = 16 .

⇒         ( x - 1 )² = 4² .

⇒           x - 1     = 4 .

⇒              x       = 4 + 1 .

⇒              x       = 5 .

Vậy x = 5 .

và :     2^x-1 = 32 .

⇒        2^x-1 = 2⁵ .

⇒       x - 1 = 5 .

⇒          x   = 5 + 1 .

⇒          x   = 6 .

Vậy x = 6 .

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

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

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

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

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

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

\(2x-1=-2\)

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

\(2x=-1\)

\(x=-1\times2\)

\(x=-2\)

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

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

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

\(49\times7^x=2401\)

   \(7^x=2401:49\)

\(7^x=49\)

\(7^x=7^2\)

\(\Rightarrow x=2\)

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

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

\(2x^x=32\)

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

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

\(\Rightarrow x^2=5\)

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

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

\(2^x\times4=32\)

\(2^x=32:4\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

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

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

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

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

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

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

\(x-x=0\)

\(\Rightarrow x=0\)

\(2^{x+1}-2^x=32\)

\(\Leftrightarrow2^x.2-2^x=2^5\)

\(\Leftrightarrow2^x.\left(2-1\right)=2^5\)

\(\Leftrightarrow2^x.1=2^5\)

\(\Leftrightarrow x=5\)

Vậy : \(x=5\)

\(2^{x+1}-2^x=32\)

\(\Leftrightarrow2^x.2-2^x=2^5\)

\(\Leftrightarrow2^x.\left(2-1\right)=2^5\)

\(\Leftrightarrow2^x=2^5\)

\(\Rightarrow x=5\)

2^x+1 -2^x =32

2^x.2 - 2^x .1 =2⁵

2^x . (2 -1) =2⁵

2^x . 1 =2⁵

^{Vay x =5}