81 : 27 = ???????
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\(3S=241+81+27+9+...+\dfrac{1}{9}+\dfrac{1}{27}\)
\(2S=3S-S=241-\dfrac{1}{81}=\dfrac{241x81-1}{81}\)
\(\Rightarrow S=\dfrac{241x81-1}{2x81}\)
Ta có :
81.27.32 = 34.33.32 = 39
813 : 272 = (34)3 : (33)2 = 312 : 36 = 36
Mà 39 > 36 ⇒ 81. 27. 32 > 813 : 272
a/
\(27^{81}=\left(3^3\right)^{81}=3^{241}\)
\(81^{27}=\left(3^4\right)^{27}=3^{108}\)
\(\Rightarrow27^{81}=3^{241}>3^{108}=81^{27}\)
b/
\(5^{60}=\left(5^3\right)^{20}=125^{20}\)
\(7^{40}=\left(7^2\right)^{20}=49^{20}\)
\(\Rightarrow5^{60}=125^{20}>49^{20}=7^{40}\)
c/
\(11^{102}=\left(11^2\right)^{51}=121^{51}>121^{50}>99^{50}\)
d. So sánh a=12^34567 với b=(12^5)^12=12^60 => a>b
so sánh b=(12^5)^12 với c=34567^12 => b>c
Vậy a>c.
(y + \(\dfrac{1}{3}\)) + ( y + \(\dfrac{1}{9}\)) + ( y + \(\dfrac{1}{27}\)) + ( y + \(\dfrac{1}{81}\)) = \(\dfrac{56}{81}\)
( y + y + y + y ) + (\(\dfrac{1}{3}\)+ \(\dfrac{1}{9}\) + \(\dfrac{1}{27}\) + \(\dfrac{1}{81}\)) = \(\dfrac{56}{81}\)
4\(y\) + ( \(\dfrac{27}{81}\) + \(\dfrac{9}{81}\) + \(\dfrac{3}{27}\) + \(\dfrac{1}{81}\) ) = \(\dfrac{56}{81}\)
4y + \(\dfrac{40}{81}\) = \(\dfrac{56}{81}\)
4y = \(\dfrac{56}{81}\) - \(\dfrac{40}{81}\)
4y = \(\dfrac{16}{81}\)
y = \(\dfrac{16}{81}\) : 4
y = \(\dfrac{4}{81}\)
\(\left(y+\dfrac{1}{3}\right)+\left(y+\dfrac{1}{9}\right)+\left(y+\dfrac{1}{27}\right)+\left(y+\dfrac{1}{81}\right)=\dfrac{56}{81}\)
\(\Rightarrow y+\dfrac{1}{3}+y+\dfrac{1}{9}+y+\dfrac{1}{27}+y+\dfrac{1}{81}=\dfrac{56}{81}\)
\(\Rightarrow4\times y+\dfrac{40}{81}=\dfrac{56}{81}\)
\(\Rightarrow4\times y=\dfrac{56}{81}-\dfrac{40}{81}\)
\(\Rightarrow4\times y=\dfrac{16}{81}\)
\(\Rightarrow y=\dfrac{16}{81}:4\)
\(\Rightarrow y=\dfrac{4}{81}\)
Ta có : 1.81=81
=> 81chia hết cho 81
Vậy 81 chữ số 1 chia hết cho 81
(81 . 19 + 81 . 27) : 81
= 81 . (19 + 27) : 81
= (81 : 81) . (19 + 27)
= 1 . 46
= 46
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