\(\dfrac{x\boxtimes7}{81}=27\)
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17 tháng 5 2021
Tham khảo link: https://olm.vn/hoi-dap/detail/55111422944.html
17 tháng 5 2021
`(x+1/3)+(x+1/9)+(x+1/27)+(x+1/81)=56/81`
`x+x+x+x+1/3+1/9+1/27=56/81-1/81`
`4x+13/27=55/81`
`4x=55/81-13/27`
`4x=55/81-52/81`
`4x=16/81`
`x=4/108`
Vậy `x=4/108`
NT
2
1 tháng 10 2021
\(x+1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}=2\)
\(\Leftrightarrow x+\dfrac{121}{81}=2\)
hay \(x=\dfrac{41}{81}\)
22 tháng 7 2021
Ta có: \(\dfrac{\left(-3\right)^x}{81}=27\)
\(\Leftrightarrow\left(-3\right)^x=2187\)
hay \(x\in\varnothing\)
29 tháng 10 2021
\(\Leftrightarrow\dfrac{\left(-3\right)^x}{3^4}=\left(-3\right)^3\\ \Leftrightarrow\left(-3\right)^x=\left(-3\right)^3\cdot\left(-3\right)^4=\left(-3\right)^7\\ \Leftrightarrow x=7\)
AH
Akai Haruma
Giáo viên
30 tháng 4 2023
Bài 1:
$(y+\frac{1}{3})+(y+\frac{1}{9})+(y+\frac{1}{27})+(y+\frac{1}{81})=\frac{56}{81}$
$(y+y+y+y)+(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81})=\frac{56}{81}$
$4\times y+\frac{40}{81}=\frac{56}{81}$
$4\times y=\frac{56}{81}-\frac{40}{81}=\frac{16}{81}$
$y=\frac{16}{81}:4=\frac{4}{81}$
AH
Akai Haruma
Giáo viên
30 tháng 4 2023
Bài 2:
$18: \frac{x\times 0,4+0,32}{x}+5=14$
$18: \frac{x\times 0,4+0,32}{x}=14-5=9$
$\frac{x\times 0,4+0,32}{x}=18:9=2$
$x\times 0,4+0,32=2\times x$
$2\times x-x\times 0,4=0,32$
$x\times (2-0,4)=0,32$
$x\times 1,6=0,32$
$x=0,32:1,6=0,2$
4 tháng 10 2021
\(a,\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}=\left(\dfrac{1}{3}\right)^3\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{1}{3}\Rightarrow x=\dfrac{5}{6}\\ b,\Rightarrow\left(\dfrac{3}{2}\right)^{2x-1}:\left(\dfrac{3}{2}\right)^9=\left(\dfrac{3}{2}\right)^4\\ \Rightarrow2x-1-9=4\\ \Rightarrow2x=14\Rightarrow x=7\\ c,\Rightarrow2^{x-1}+2^{x+2}=9\cdot2^5\\ \Rightarrow2^{x-1}\left(1+2^3\right)=9\cdot2^5\\ \Rightarrow2^{x-1}\cdot9=9\cdot2^5\\ \Rightarrow2^{x-1}=2^5\Rightarrow x-1=5\Rightarrow x=6\\ d,\Rightarrow\left(2x+1\right)^2=12+69=81\\ \Rightarrow\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
29 tháng 11 2023
\(3S=241+81+27+9+...+\dfrac{1}{9}+\dfrac{1}{27}\)
\(2S=3S-S=241-\dfrac{1}{81}=\dfrac{241x81-1}{81}\)
\(\Rightarrow S=\dfrac{241x81-1}{2x81}\)
22 tháng 7 2023
\(a) \sqrt{4x^2− 9} = 2\sqrt{x + 3}\)
\(ĐK:x\ge\dfrac{3}{2}\)
\(pt\Leftrightarrow4x^2-9=4\left(x+3\right)\)
\(\Leftrightarrow4x^2-9=4x+12\)
\(\Leftrightarrow4x^2-4x-21=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1-\sqrt{22}}{2}\left(l\right)\\x=\dfrac{1+\sqrt{22}}{2}\left(tm\right)\end{matrix}\right.\)
\(b)\sqrt{4x-20}+3.\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
\(ĐK:x\ge5\)
\(pt\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)
\(\Leftrightarrow2\sqrt{x-5}=4\Leftrightarrow\sqrt{x-5}=2\)
\(\Leftrightarrow x-5=4\Leftrightarrow x=9\left(tm\right)\)
22 tháng 7 2023
\(c)\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27.\sqrt{\dfrac{x-1}{81}}=4\)
ĐK:x>=1
\(pt\Leftrightarrow2\sqrt{x-1}-\sqrt{x-1}+3\sqrt{x-1}=4\)
\(\Leftrightarrow4\sqrt{x-1}=4\Leftrightarrow\sqrt{x-1}=1\)
\(\Leftrightarrow x-1=1\Leftrightarrow x=2\left(tm\right)\)
\(d)5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)
\(ĐK:x\ge3\)
\(pt\Leftrightarrow3\sqrt{x-3}-\dfrac{14}{3}\sqrt{x-3}-7\sqrt{x^2-9}+6\sqrt{x^2-9}=0\)
\(\Leftrightarrow-\dfrac{5}{3}\sqrt{x-3}-\sqrt{x^2-9}=0\Leftrightarrow\dfrac{5}{3}\sqrt{x-3}+\sqrt{x^2-9}=0\)
\(\Leftrightarrow(\dfrac{5}{3}+\sqrt{x+3})\sqrt{x-3}=0\)
\(\Leftrightarrow\sqrt{x-3}=0\) (vì \(\dfrac{5}{3}+\sqrt{x+3}>0\))
\(\Leftrightarrow x-3=0\Leftrightarrow x=3\left(nhận\right)\)
9 tháng 9 2017
a/ \(27^x.9^x=9^{27}:81\)
\(\Leftrightarrow3^{3x}.3^{2x}=3^{54}:3^4\)
\(\Leftrightarrow3^{2x+3x}=3^{50}\)
\(\Leftrightarrow2x+3x=50\)
\(\Leftrightarrow5x=50\)
\(\Leftrightarrow x=10\)
Vậy ...
C
9 tháng 9 2017
\(a.27^x.9^x=9^{27}:81\)
\(\left(3^3\right)^x.\left(3^2\right)^x=\left(3^2\right)^{27}:\left(3^2\right)^2\)
\(3^{3x}.3^{2x}=3^{50}\)
\(3^{3x+2x}=3^{50}\)
\(\Rightarrow3x+2x=50\)
\(x\left(3+2\right)=50\)
\(x=50:5=10\)
Vậy\(x=10\)
\(b.\left(\dfrac{12}{25}\right)^x=\left(\dfrac{5}{3}\right)^{-2}-\left(-\dfrac{3}{5}\right)^4\)
\(\left(\dfrac{12}{25}\right)^x=\dfrac{9}{25}-\dfrac{81}{625}\)
\(\left(\dfrac{12}{25}\right)^x=\dfrac{144}{625}\)( Đề sai )
MA
2
MA
18 tháng 12 2017
Akai Haruma Nguyễn Huy Tú Nguyễn Huy ThắngHồng Phúc NguyễnPhạm Hoàng Giang......và nhiều bạn nữa giúp mik vs
18 tháng 12 2017
\(\dfrac{3}{x^2+6x+9}+\dfrac{2}{6x-x^2-9}+\dfrac{x^2+30x-27}{x^4-18x^2+81}\)
\(=\dfrac{3}{\left(x+3\right)^2}+\dfrac{-2}{\left(x-3\right)^2}+\dfrac{x^2+30x-27}{x^4-9x^2-9x^2+81}\)
\(=\dfrac{3}{\left(x+3\right)^2}-\dfrac{2}{\left(x-3\right)^2}+\dfrac{x^2+30x-27}{\left(x-3\right)^2\left(x+3\right)^2}\)
\(=\dfrac{3\left(x-3\right)^2}{\left(x+3\right)^2\left(x-3\right)^2}-\dfrac{2\left(x+3\right)^2}{\left(x+3\right)^2\left(x-3\right)^2}+\dfrac{x^2+30x-27}{\left(x-3\right)^2\left(x+3\right)^2}\)
\(=\dfrac{3x^2-18x+27-2x^2-12x-18+x^2+30x-27}{\left(x-3\right)^2\left(x+3\right)^2}\)
\(=\dfrac{2x^2-18}{\left(x-3\right)^2\left(x+3\right)^2}\)
\(=\dfrac{2\left(x^2-9\right)}{\left(x-3\right)^2\left(x+3\right)^2}\)
\(=\dfrac{2\left(x-3\right)\left(x+3\right)}{\left(x-3\right)^2\left(x+3\right)^2}\)
\(=\dfrac{2}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x^2-9}\)
\(x\times7\div81=27\)
\(x\times7=27\times81\)
\(x\times7=2187\)
\(x=\dfrac{2187}{7}\)