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\(a=15^{120}:25^{60}\)
\(a=3^{120}.5^{120}:\left(5^2\right)^{60}\)
\(a=3^{120}.5^{120}:5^{120}\)
\(a=3^{120}\)
\(b=2^{45}.2^{15}.4^{60}\)
\(b=2^{60}.\left(2^2\right)^{60}\)
\(b=2^{60}.2^{120}\)
\(b=2^{180}\)
ta co \(a=3^{120}=\left(3^2\right)^{60}=9^{60}\)
\(b=2^{180}=\left(2^3\right)^{60}=8^{60}\)
vi \(9^{60}>8^{60}\) nen \(3^{120}>2^{180}\)
vay \(a>b\)
\(a=\left(15^2\right)^{60}:25^{60}\)
\(a=225^{60}:25^{60}\)
\(a=\left(225:25\right)^{60}=9^{60}\)
\(b=2^{45}.2^{15}.2^{120}\)
\(b=2^{180}=8^{60}\)
vì \(8^{60}< 9^{60}\)nên b<a
1,\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^{-4}\)
\(\Rightarrow\)2x+7=-4
2x=-11
x=-5,5
a) ta có A=\(15^{120}:25^{60}=3^{120}.5^{120}:5^{120}=3^{120}=9^{60}\)
B=\(2^{45}.2^{15}.4^{60}=2^{60}.2^{120}=2^{180}=8^{60}\)
-> A<B
b) bạn chỉ cần tính từng cái ra là dc ý ,ak dễ lắm nếu bạn chăm chỉ
Bài làm:
Ta có: \(a=15^{120}\div25^{60}\)
\(a=15^{120}\div5^{120}\)
\(a=3^{120}=9^{60}\)
và \(b=2^{45}.2^{15}.4^{60}\)
\(b=2^{60}.2^{120}\)
\(b=2^{180}=8^{60}\)
Mà \(9^{60}>8^{60}\Rightarrow a>b\)
a) Ta có: \(25^{15}=\left(5^2\right)^{15}=5^{30}\)
\(8^{10}.3^{30}=\left(2^3\right)^{10}.3^{30}\)\(=2^{30}.3^{30}=6^{30}\)
Vì \(5^{30}< 6^{30}\)nên \(25^{15}< 8^{10}.3^{30}\)
b) Ta có: \(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)
\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{\left(2^3\right)^{10}.3^{30}}{7^{30}.\left(2^2\right)^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{3^{30}}{7^{30}}\)
Vì \(2^{30}< 3^{30}\)nên \(\frac{2^{30}}{7^{30}}< \frac{3^{30}}{7^{30}}\)hay \(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)
_Học tốt_
a) 2515 và 810. 330
2515 = (52 ) 15 = 530
810. 330 = (23 )10. 330 = 230. 330 = 630
Vì 530< 630
nên 2515< 810. 330
b) \(\frac{4^{15}}{7^{30}}\)và \(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)
\(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)
\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{\left(2^3\right)^{10}.3^{30}}{7^{30}.\left(2^2\right)^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{3^{30}}{7^{30}}\)
Vì \(\frac{2^{30}}{7^{30}}< \frac{3^{30}}{7^{30}}\)
nên \(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)
a)\(25^{15}=5^{2^{15}}=5^{30}\)
\(8^{10}.3^{30}=2^{3^{10}}.3^{30}=\left(2.3\right)^{30}=6^{30}\)
\(5^{30}< 6^{30}=>25^{15}< 8^{10}.3^{30}\)
b)\(\frac{4^{15}}{7^{30}}=\frac{2^{2^{15}}}{7^{30}}=\frac{2^{30}}{7^{30}}=\left(\frac{2}{7}\right)^{30}\)
\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{6^{30}}{14^{30}}=\left(\frac{6}{14}\right)^{30}=\left(\frac{3}{7}\right)^{30}\)
Vì hai số có mũ bằng 30 nên ta so sánh :\(\frac{2}{7}< \frac{3}{7}\)
=>\(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\).
Ta có: a = 15^120:25^60
a = (15^2)^60: 25^60
a = 225^60 : 25^60
a = (225 : 25)^60
a = 9^60 (1)
Lai co b = (2^45)(2^15)(4^60)
b = [ (2^45)(2^15) ].(4^60)
b = (2^60).(4^60)
b = (2.4)^(60)
b = 8^60 (2)
Từ (1) và (2) => a > b