Question

[Lala]

Tìm số tự nhiên x biết:

a) 3^x + 3^x+1 + 3^x+2 = 1003

b) 5^x . 5¹⁹= 5²⁰. 5¹¹

c) x²⁰⁰⁵ = x

Answer 1

[Trai Vô Đối]

HỌC TỐT NHÉ

c,\(x^{2005}=x\Leftrightarrow\left[{}\begin{matrix}x^{2005}=x=0\\x^{2005}=x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

b,\(5^x.5^{19}=5^{20}.5^{11}\Leftrightarrow5^{x+19}=5^{20+11}\Leftrightarrow x+19=31\Leftrightarrow x=12\)

a,Cau nay hinh nhu sai de ban a 3\(^x\)+\(3^{x+1}+3^{x+2}=1003\)\(\Leftrightarrow3^x.1+3^x.3+3^x.3^2=1003\Leftrightarrow3^x.\left(1+3+9\right)=1003\Leftrightarrow3^x.13=1003\Leftrightarrow3^x=\dfrac{1003}{13}\)

Answer 2

[Mashiro Shiina]

\(3^x+3^{x+1}+3^{x+2}=1003\)

\(3^x.1+3^x.3+3^x.3^2=1003\)

\(3^x\left(1+3+3^2\right)=1003\)

\(3^x.13=1003\)

\(3^x=\dfrac{1003}{13}\)

..........

\(5^x.5^{19}=5^{20}.5^{11}\)

\(5^x.5^{19}=5^{31}\)

\(5^x=5^{12}\Rightarrow x=12\)

\(x^{2005}=x\Rightarrow x=\left\{0;1;-1\right\}\)