So sánh A=[6.(-1/3)^2-(-1/3)+1]:(-1/3-1) và B=(729-1^3) (729-2^3) (729-3^3)...(729-125^3)
cho biểu thức:A=[6\(\times\left(-\frac{1}{3}\right)^2-3\times\left(-\frac{1}{3}\right)+1\)]\(\div\left(-\frac{1}{3}-1\right)\)
B=\(\left(729-1^3\right)\times\left(729-3^3\right)\times...\times\left(729-125^3\right)\)
hãy so sánh A và B
nhanh lên mai mình phải nộp rồi
Ta có: \(A=\left[6.\left(-\frac{1}{3}\right)^2-3.\left(-\frac{1}{3}\right)+1\right]:\left(\frac{-1}{3}-1\right)\)
\(=\left(6.\frac{1}{9}-\left(-1\right)+1\right):\left(\frac{-4}{3}\right)\)
\(=\left(\frac{2}{3}+2\right).\left(\frac{-3}{4}\right)\)
\(=\frac{8}{3}.\left(-\frac{3}{4}\right)\)
\(=-2\)
\(B=\left(729-1^3\right)\left(729-3^3\right)...\left(729-125^3\right)\)
\(\Rightarrow B=\left(729-1^3\right)\left(729-3^3\right)...\left(729-9^3\right)...\left(729-125^3\right)\)
\(\Rightarrow B=\left(729-1^3\right)\left(729-3^3\right)...0...\left(729-125^3\right)\)
\(\Rightarrow B=0\)
Vì -2 < 0 nên A < B
Vậy A < B
1+1/3+1/27+1/81+1/243+1/729+1/2187 = ?
A.1093/2187 B.1/729 C.1093/729 D.2186/729
viết sai rồi
tìm x biết/1/729 =(1+1/3+19+...+1/729)x
a) (1/3)^x = 1/729
b) (1/3-1/2)^x-1 = 1/36
c) 25/5^x =1/125
d) (-7)^2n-1/49 = -343
a)\(\dfrac{1}{3}^x=\dfrac{1}{729}\)
\(\dfrac{1}{3}^x=\dfrac{1}{3}^6\)
Suy ra x=6
vậy x=6
b)\(\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^x=\dfrac{1}{36}\)
\(\left(-\dfrac{1}{6}\right)^x\)=\(\dfrac{1}{6}^2\)
Do đó x=2
Vậy x=2
c)\(\dfrac{25}{5}^x=\dfrac{1}{125}\)
\(5^x=5^{-3}\)
Suy ra x=-3
Vậy x=-3
d)\(7^{2n-\dfrac{1}{49}}=-343\)
\(-7^{2n-\dfrac{1}{49}}=-7^3\)
Do đó \(2n-\dfrac{1}{49}=3\)
2n=\(\dfrac{148}{49}\)
n=\(\dfrac{74}{49}\)
vậy n=\(\dfrac{74}{49}\)
chúc bạn học tốt ạ
Tính giá trị biểu thức:
a) A= 3 + 3^2 + 3^3 + 3^4 +...+3^100
b) B=5 x 4^15 x 9^9 - 4 x 3^20 x 8^9
____________________________
5 x 2^9 x 6^19 - 7 x 2^29 x 27^6
c) 2181 x 729 + 729 x 27^2
_____________________________
3^2 x 9^2 x 243 + 3^6x 162 x 12 + 723 x 729
d) 1 + 1 + 1 + ..... + 1 + 1
__ __ __ __ ___
1 x2 2 x 3 3 x 4 98 x99 99 x 100
trong đó có ___ để ghi phân số ^ là số mũ
1, Tìm x
a, (2^x)^5 : 4^3 = 8^15
b, (3^2)^x . 9^3 = 243^9
c, ( 1/125)^3 . 5^x = 25^5
d, 1/81: 3^x = 1/729
e, ( 5x-2)^4 = 16^8
a) (2x)5 : 43 = 815 => 25x = 815.43 = (23)15.(22)3 = 245.26 = 251 => 5x = 51 => x = 10,2
b) (32)x .93 = 2439 => 32x = 2439 : 93 = (35)9 : (32)3 = 345 : 36 = 339 => 2x = 39 => x = 19,5
c) (1/125)3.5x = 255 => 5x = 255 : (1/125)3 = (52)5 : (1/53)3 = 510 : (5-3)3 = 510 : 5-9 = 519 => x = 19
d) 1/81 : 3x = 1/729 => 3x = 1/81 : 1/729 = 1/34.729 = 3-4.36 = 32 => x = 2
e) (5x - 2)4 = 168 = (162)4 = 2564
=> 5x - 2 = -256 ; 256 => 5x = -254 ; 258 => x = -50,8 ; 51,6
P/S : Thay x = 10,2 vào câu a , x = 19,5 vào câu b sẽ thấy điều hư cấu : 210,2 và 919,5.Ko thể tính được giá trị của 2 lũy thừa này.
Tìm x
3^x . 3^x+1 . 3^x+2 ≥ 729
3^{x}.3^{x+1}.3^{x+2}>=729`
`=>3^{x+x+1+x+2}>=3^6`
`=>3^{3x+3}>=3^6`
`=>3x+3>=6`
`=>3x>=3=>x>=1`
BÀI TÍNH NHANH
A.2/3+2/6+2/12+2/24+2/48+2/96+2/192
B.1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
C.1/3+1/9+1/27+1/81+1/243+1/729
D.3/2+3/8+3/32+3/128+3/512
E.3+3/5+3/25+3/125+3/625
a) = \(\frac{127}{96}\)
b) = \(\frac{255}{256}\)
c) Mik bỏ nha
d) = \(\frac{1023}{512}\)
e) = \(\frac{2343}{625}\)
Tìm X:(X+1/3)+(X+1/9)+(X+1/27)+...+(X+1/729)=4209/729
Giups mình với các bạn.
`Answer:`
\(\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{9}\right)+\left(x+\frac{1}{27}\right)+...+\left(x+\frac{1}{729}\right)=\frac{4209}{729}\)
\(\Leftrightarrow\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{3^2}\right)+\left(x+\frac{1}{3^3}\right)+...+\left(x+\frac{1}{3^6}\right)=\frac{4209}{729}\)
\(\Leftrightarrow6x+\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\right)=\frac{4209}{729}\text{(*)}\)
Đặt \(N=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\)
\(\Leftrightarrow3N=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^5}\)
\(\Leftrightarrow3N-N=\left(1+\frac{1}{3}+\frac{1}{3^2}+..+\frac{1}{3^5}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\right)\)
\(\Leftrightarrow2N=1-\frac{1}{3^6}\)
\(\Leftrightarrow2N=\frac{728}{729}\)
\(\Leftrightarrow N=\frac{364}{729}\)
\(\text{(*)}\Leftrightarrow6x+\frac{364}{729}=\frac{4209}{729}\)
\(\Leftrightarrow6x=\frac{3845}{729}\)
\(\Leftrightarrow x=\frac{3845}{4374}\)