Có 5149=599+50=599 x 550
mà 599 > 1199
=> 5149 > 1199
k hộ mik nha!
Hình như bạn sai. 5^99<11^99 mà.
Mình có cách này, không thuận tiện lắm nhưng có thể nói là tạm dùng được để so sánh.
Ta có:
\(11^{99}\)
\(=\left[11^{99}\div10^{99}\div\left(\frac{11}{10}\right)^{49}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left[\left(\frac{11}{10}\right)^{99}\div\left(\frac{11}{10}\right)^{49}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left(\frac{11}{10}\right)^{50}\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(5^{149}\)
\(=\left[5^{149}\div10^{99}\div\left(\frac{11}{10}\right)^{49}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left[5^{149}\div5^{99}\div2^{99}\div\left(\frac{11}{10}\right)^{49}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left[5^{50}\div2^{50}\div2^{49}\div\left(\frac{11}{10}\right)^{49}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left\{\left(5^{50}\div2^{50}\right)\div\left[2^{49}\cdot\left(\frac{11}{10}\right)^{49}\right]\right\}\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left[\left(\frac{5}{2}\right)^{50}\div\left(\frac{11}{5}\right)^{49}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(=\left[\left(\frac{5}{2}\right)^{50}\div\left(\frac{11}{5}\right)^{50}\cdot\frac{11}{5}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
\(\left[\left(\frac{25}{22}\right)^{50}\cdot\frac{11}{5}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\)
Mà \(\frac{25}{22}>\frac{11}{10}\Rightarrow\left[\left(\frac{25}{22}\right)^{50}\cdot\frac{11}{5}\right]\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]>\left(\frac{11}{10}\right)^{50}\cdot\left[10^{99}\cdot\left(\frac{11}{10}\right)^{49}\right]\Rightarrow5^{149}>11^{99}\)
Khi nào nghĩ được cách hay hơn mình sẽ đăng tiếp. k mình nha.
Mk vừa nghĩ ra cách này hay hơn:
Có 5^149.55=5^150.11
11^99.55=11^100.5
Ta có 5^150=125^50; 11^100=121^50
Có 125^50>121^50 nên 5^150>11^100
Mà 11>5 nên 5^150.11>11^100.5
Nên 5^149.55>11^99.55 nên 5^149>11^99
Vậy 5^149>11^99
