Question

tìm x |x+\(\dfrac{2}{3}\)|+2=\(\dfrac{7}{3}\)

so sánh các số \(^{25^{50}}\)và \(^{5^{300}}\)

cho A=3+ 3^2+3^3+....+3^2008.Tìm x biết 2A+3=3^x

Answer 1

a, \(\)\(\left|x+\dfrac{2}{3}\right|+2=\dfrac{7}{3}\)

⇔\(\left|x+\dfrac{2}{3}\right|=\dfrac{7}{3}-2\)

⇔\(\left|x+\dfrac{2}{3}\right|=\dfrac{1}{3}\)

⇔\(\left[{}\begin{matrix}x+\dfrac{2}{3}=\dfrac{1}{3}\Rightarrow x=\dfrac{1}{3}-\dfrac{2}{3}\Rightarrow x=\dfrac{-1}{3}\\x+\dfrac{2}{3}=\dfrac{-1}{3}\Rightarrow x=\dfrac{-1}{3}-\dfrac{2}{3}\Rightarrow x=\left(-1\right)\end{matrix}\right.\)

Vậy x = \(\dfrac{-1}{3}\) hoặc x = (-1) thì \(\left|x+\dfrac{2}{3}\right|+2=\dfrac{7}{3}\)

b,

Xét \(25^{50}\) và \(5^{300}\) ta có:

\(25^{50}=\left(5^2\right)^{50}=5^{100}\)

\(5^{300}=\left(5^3\right)^{100}=125^{100}\)

Vì \(5^{100}< 125^{100}\) nên \(25^{50}< 5^{300}\)