\(5^{300}=\left(5^3\right)^{100}=125^{100};3^{500}=\left(3^5\right)^{100}=243^{100}\)
mà 125<243
nên \(5^{300}< 3^{500}\)
\(\left(\dfrac{5}{3}\right)^2:x=\dfrac{5}{2}\)
=>\(\dfrac{25}{9}:x=\dfrac{5}{2}\)
=>\(x=\dfrac{25}{9}:\dfrac{5}{2}=\dfrac{25}{9}\cdot\dfrac{2}{5}=\dfrac{50}{45}=\dfrac{10}{9}\)
`5^300 = 5^(3.100) = (5^3)^100 = 125^100`
`3^500 = 3^(5.100) = (3^5)^100 = 243^100`
Do `125 < 243 => 125^100 < 243^100 => 5^300 < 3^500`
Vậy `5^300 < 3^500`
-------------------
`(5/3)^2 : x = 5/2`
`<=> 25/9 : x = 5/2`
`<=> x= 25/9 : 5/2`
`<=> x = 25/9 . 2/5`
`<=> x = 10/9`
Vậy `x = 10/9`
