5^x+1-5^x=500

(5^x-5^x)+1=500

0.5^x=499

Sai đề

5^x + 1 - 5^x = 500

=> 5^x - (-1) - 5^x = 500

=> 5^x - 5^x - (-1) = 500

=> 0 - (-1) = 500

=> 1 = 500

=> Sai đề

\(\frac{2x-3}{2}=\frac{32}{2x-3}\)

\(\Rightarrow\left(2x-3\right).\left(2x-3\right)=2.32\)

\(\left(2x-3\right)^2=64=8^2=\left(-8\right)^2\)

=> 2x-3 = 8 => 2x = 11 => x = 11/2

2x -3 = -8 => 2x = -5 => x = -5/2

KL:...

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

\(\Leftrightarrow\left(x^2-2x+1\right)-\left(x-1\right)=0\)

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

\(\Leftrightarrow\left(x-1\right)\left[\left(x-1\right)-1\right]=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}}\)

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

\(x^{11}:\left(-x\right)^{10}\)

\(=x^{11}:x^{10}\)

\(=x\)

Ta có : x¹¹ : ( -x ) ¹⁰

          = x¹¹ : x¹⁰

        = x¹⁰  .x : x¹⁰ 

        = x 

\(3,2\times x+\left(-1,2\right)\times x+2,7=-4,9\)

\(\left(3,2-1,2\right)x=-4,9-2,7\)

\(2x=-7,6\)

x=-3,8

ko biết

\(\left|x\right|+x=0\Rightarrow\left|x\right|=-x\Rightarrow x\le0\)

2^x.(1+2+4+8)=120

2^x.15=120

2^x=120:15

2^x=8

2^x=2^3

x=3

Vậy x=3

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}\)

\(\left(2^x+2^{x+1}\right)+\left(2^{x+2}+2^{x+3}\right)\)

\(=\left(2^x+2^x\cdot2\right)+\left(2^x\cdot4+2^{x+3}\cdot8\right)\)

\(=2^x\cdot3+2^x\cdot12=2^x\cdot15\)

\(2^x\cdot15=120\)

\(2^x=8\)

\(x=3\)