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\left(3.x+3\right)^{3}=729(3.x+3)3=729
K
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SG
4
26 tháng 6 2017
\(\left(\frac{3^x}{3}\right)^2=\frac{1}{729}\Rightarrow3^{x-1}=\frac{1}{27}\Rightarrow x-1=-3\Rightarrow x=-2\)
26 tháng 2 2017
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
13 tháng 8 2018
3^ x . 3^ 2= 729
3^ x . 9 = 729
3^ x = 729: 9
3^x =81
vậy x = 3^3
5^ x . 625 = 3125
5^x = 3125:625
5^x = 5
vậy x = 1
( 2x+1 )^ 3 = 27
( 2x+1) ^ 3 = 3^3
vậy 2x+1 = 3
vậy x = 0
AH
Akai Haruma
Giáo viên
15 tháng 8 2018
Lời giải:
a) \((5x-1)^6=729=3^6=(-3)^6\)
\(\Rightarrow \left[\begin{matrix} 5x-1=3\\ 5x-1=-3\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{4}{5}\\ x=\frac{-2}{5}\end{matrix}\right.\)
b)
\(\frac{8}{25}=\frac{2^x}{5^{x-1}}=\frac{2^x}{5^x:5}=5.(\frac{2}{5})^x\)
\(\Rightarrow \frac{8}{125}=(\frac{2}{5})^x\)
\(\Rightarrow (\frac{2}{5})^3=(\frac{2}{5})^x\Rightarrow x=3\)
c)
\((\frac{1}{16})^x=(\frac{1}{2})^{10}\)
\(\Rightarrow (\frac{1}{2^4})^x=(\frac{1}{2})^{10}\)
\(\Rightarrow (\frac{1}{2})^{4x}=(\frac{1}{2})^{10}\Rightarrow 4x=10\Rightarrow x=\frac{5}{2}\)
d)
\(9^{x}:3^x=3\Rightarrow (\frac{9}{3})^x=3\)
\(\Rightarrow 3^x=3^1\Rightarrow x=1\)
B
14 tháng 8 2018
a) \(\left(5x-1\right)^6=729\)
\(\Leftrightarrow5x-1=3\)
\(\Leftrightarrow5x=4\)
\(\Leftrightarrow x=\dfrac{4}{5}\)
21 tháng 8 2022
b: \(\Leftrightarrow\dfrac{2^3}{5^2}=\dfrac{2^x}{5^{x-1}}\)
=>x=3 và x-1=2
=>x=3
c: \(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{10}\)
=>4x=10
=>x=5/2
d: =>3x=3
=>x=1
Y
14 tháng 8 2018
a) \(\left(5x-1\right)^6=729\)
\(\Rightarrow\left[{}\begin{matrix}\left(5x-1\right)^6=3^6\\\left(5x-1\right)^6=\left(-3\right)^6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}5x-1=3\\5x-1=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}5x=4\\5x=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{2}{5}\end{matrix}\right.\)
b) \(\dfrac{8}{25}=\dfrac{2^x}{5^{x-1}}\)
\(\Rightarrow\left[{}\begin{matrix}2^x=2^3\\5^{x-1}=5^2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x-1=2\end{matrix}\right.\)
\(\Rightarrow x=3\)
Vậy x = 3
c) \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{2}\right)^{10}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{3x}=\left(\dfrac{1}{2}\right)^{10}\)
\(\Rightarrow3x=10\)
\(\Rightarrow x=\dfrac{10}{3}\)
d) \(9^x:3^x=3\)
\(\Rightarrow\left(9:3\right)^x=3\)
\(\Rightarrow3^x=3^1\)
\(\Rightarrow x=1\)
NK
14 tháng 8 2018
a,\(\left(5x-1\right)^6=729\)
\(\left(5x-1\right)^6=3^6\)
\(5x-1=3\)
\(5x=4\)
\(x=\dfrac{4}{5}\)
NK
14 tháng 8 2018
b Ta có \(8=2^3\),\(25=5^2\)
Mà \(\dfrac{8}{25}=\dfrac{2^x}{5^{x-1}}\)
=> \(2^3=2^x,5^2=5^{x-1}\)
=> x=3
KN
16 tháng 2 2020
Ta có: \(A=\left[6.\left(\frac{-1}{3}\right)^2-\left(-\frac{1}{3}\right)+1\right]:\left(\frac{-1}{3}-1\right)\)
\(\Rightarrow A=\left[6.\frac{1}{9}+\frac{1}{3}+1\right]:\left(\frac{-1}{3}-\frac{3}{3}\right)\)
\(\Rightarrow A=\left[\frac{2}{3}+\frac{1}{3}+1\right]:\frac{-4}{3}\)
\(\Rightarrow A=\left[1+1\right].\frac{-3}{4}=2.\frac{-3}{4}=\frac{-3}{2}\)
Mà \(B=\left(729-1^3\right)\left(729-2^3\right)\left(729-3^3\right)...\left(729-125^3\right)\)
\(=\left(729-1^3\right)\left(729-2^3\right)...\left(729-9^3\right)...\left(729-125^3\right)\)
\(=\left(729-1^3\right)\left(729-2^3\right)...0...\left(729-125^3\right)=0\)
Vì \(\frac{-3}{2}< 0\)nên A < B
HD
0
26 tháng 8 2021
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`
giúp mik với cảm ơn nhiều !!!
3.x+3=729
=> 3.(x+1)=729
=> x+1=729 : 3
=> x+1=243
=> x=243-1
=> x=242