Tìm số nguyên x, biết:
\(4\times3^{x-2}+2\times3^{x+1}=4\times3^4+2\times3^7\)
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GL
24 tháng 8 2023
a) \(\dfrac{2}{5}=\dfrac{2\times3}{5\times3}=\dfrac{6}{15}=\dfrac{2}{5}\)
\(\dfrac{4}{7}=\dfrac{4\times2}{7\times2}=\dfrac{8}{14}=\dfrac{4}{7}\)
\(\dfrac{13}{54}=\dfrac{13\times3}{54\times3}=\dfrac{39}{162}=\dfrac{13}{54}\)
b) \(\dfrac{8}{20}=\dfrac{8:4}{20:4}=\dfrac{2}{5}\)
\(\dfrac{10}{16}=\dfrac{10:2}{16:2}=\dfrac{5}{8}\)
\(\dfrac{25}{65}=\dfrac{25:5}{65:5}=\dfrac{5}{13}\)
DT
1
NH
2
28 tháng 6 2015
3^x = 3^3.3^5
3^x = 3^ (5 +3)
3^x = 3^5
=> x = 5
2, 2^x = 4 .128
2^x = 2^2 . 2^7
2^x = 2^ ( 2 +7)
2^x = 2^9
=> x = 9
3, 2^x.3^x = 2^2 . 3^2
=> x = 2
28 tháng 6 2015
3^x = 3^3.3^5
3^x = 3^ (5 +3)
3^x = 3^5
=> x = 5
2, 2^x = 4 .128
2^x = 2^2 . 2^7
2^x = 2^ ( 2 +7)
2^x = 2^9
=> x = 9
3, 2^x.3^x = 2^2 . 3^2
=> x = 2
BT
30 tháng 3 2017
A=\(\frac{5x\left(2^2x3^2\right)^9-2x\left(2^2x3\right)^{14}x3^4}{5x2^{28}x3^{18}-7x2^{29}x3^{18}}\)=\(\frac{5x2^{18}x3^{18}-2x2^{28}x3^{14}x3^4}{2^{28}x3^{18}x\left(5-7x2\right)}\)=\(\frac{5x2^{18}x3^{18}-2^{29}x3^{18}}{2^{28}x3^{18}x\left(-9\right)}\)=
= \(\frac{2^{18}x3^{18}\left(5-2^{11}\right)}{-9x2^{28}x3^{18}}=\frac{5-2^{11}}{-9x2^{10}}=\frac{2043}{9216}=\frac{227}{1024}\)
LT
1
14 tháng 10 2018
\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=6^x\)
\(\Rightarrow\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}=6^x\)
\(\Leftrightarrow\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}=6^x\)
\(\Leftrightarrow\dfrac{3.8}{4}=6^x\)
\(\Leftrightarrow6^1=6^x\)
\(\Leftrightarrow x=1\)
Vậy..
16 tháng 3 2017
a) \(\left(\dfrac{x}{2}-\dfrac{1}{3}\right)^2=\sqrt{16}\) \(\Rightarrow\left(\dfrac{x}{2}-\dfrac{1}{3}\right)^2=4\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{2}-\dfrac{1}{3}=-2\\\dfrac{x}{2}-\dfrac{1}{3}=2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{2}=\dfrac{-5}{3}\\\dfrac{x}{2}=\dfrac{7}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-10}{3}\\x=\dfrac{14}{3}\end{matrix}\right.\)
Vậy \(x=\dfrac{-10}{3}\) hoặc \(x=\dfrac{14}{3}\) thì thỏa mãn đề bài.
b) \(\dfrac{x+4}{2010}+\dfrac{x+3}{2011}=\dfrac{x+2}{2012}+\dfrac{x+1}{2013}\) \(\Rightarrow\left(\dfrac{x+4}{2010}+1\right)+\left(\dfrac{x+3}{2011}+1\right)=\left(\dfrac{x+2}{2012}+1\right)+\left(\dfrac{x+1}{2013}+1\right)\) \(\Rightarrow\dfrac{x+4+2010}{2010}+\dfrac{x+3+2011}{2011}=\dfrac{x+2+2012}{2012}+\dfrac{x+1+2013}{2013}\) \(\Rightarrow\dfrac{x+2014}{2010}+\dfrac{x+2014}{2011}=\dfrac{x+2014}{2012}+\dfrac{x+2014}{2013}\) \(\Rightarrow\dfrac{x+2014}{2010}+\dfrac{x+2014}{2011}-\dfrac{x+2014}{2012}-\dfrac{x+2014}{2013}=0\) \(\Rightarrow\left(x+2014\right)\times\left(\dfrac{1}{2010}+\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}\right)=0\) \(\Rightarrow x+2014=0\) \(\Rightarrow x=-2014\)
Vậy \(x=-2014\) thì thỏa mãn đề bài.
c) \(3^{x+2}+4\times3^{x+1}=7\times3^6\) \(\Rightarrow3^{x+1+1}+4\times3^{x+1}=7\times3^6\) \(\Rightarrow3^{x+1}\times3+4\times3^{x+1}=7\times3^6\) \(\Rightarrow\left(3+4\right)\times3^{x+1}=7\times3^6\) \(\Rightarrow3^{x+1}=3^6\) \(\Rightarrow x+1=6\) \(\Rightarrow x=5\)
Vậy \(x=5\) thì thỏa mãn đề bài.
T
16 tháng 3 2017
a)
\(\left(\dfrac{x}{2}-\dfrac{1}{3}\right)^2=\sqrt{16}\\ \Rightarrow\left(\dfrac{x}{2}-\dfrac{1}{3}\right)^2=4\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{x}{2}-\dfrac{1}{3}=2\\\dfrac{x}{2}-\dfrac{1}{3}=-2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{2}=\dfrac{1}{3}+2\\\dfrac{x}{2}=\dfrac{1}{3}-2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{2}=\dfrac{7}{3}\\\dfrac{x}{2}=\dfrac{-5}{3}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{3}.2\\x=\dfrac{-5}{3}.2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{14}{3}\\x=\dfrac{-10}{3}\end{matrix}\right.\)
b)
\(\dfrac{x+4}{2010}+\dfrac{x+3}{2011}=\dfrac{x+2}{2012}+\dfrac{x+1}{2013}\)
\(\Rightarrow\dfrac{x+4}{2010}+1+\dfrac{x+3}{2011}+1=\dfrac{x+2}{2012}+1+\dfrac{x+1}{2013}+1\)
\(\Rightarrow\dfrac{x+2014}{2010}+\dfrac{x+2014}{2011}=\dfrac{x+2014}{2012}+\dfrac{x+2014}{2013}\)
\(\Rightarrow\dfrac{x+2014}{2010}+\dfrac{x+2014}{2011}-\dfrac{x+2014}{2012}-\dfrac{x+2014}{2013}=0\)
\(\Rightarrow\left(x+2014\right)\left(\dfrac{1}{2010}+\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}\right)=0\)
mà \(\dfrac{1}{2010}+\dfrac{1}{2011}-\dfrac{1}{2012}-\dfrac{1}{2013}\ne0\)
=> x + 2014 = 0
=> x = -2014
vậy x = -2014
c)\(3^{x+2}+4.3^{x+1}=7.3^6\)
\(\Rightarrow3^{x+1}.3+4.3^{x+1}=7.3^6\\ \Rightarrow3^{x+1}\left(3+4\right)=7.3^6\\ \Rightarrow3^{x+1}.7=7.3^6\\ \Rightarrow3^{x+1}=3^6\\ \Rightarrow x+1=6\\ x=6-1\\ x=5\)
vậy x = 5
15 tháng 5 2015
dau . la dau x
a/ 1.3.2.4.3.5.4.6.5.7/2.2.3.3.4.4.5.5.6.6=1.7/2.6=7/12
b/ ab.aba=abab
aba=abab:ab
aba=101
=>a=1 b=0
aabb : ab = 99 hay ab x 99 = aabb hay ab x100 – ab = aabb
Ta có phép tính
__ ab00
___ab___
aabb
b=0 hoặc b=5
Nếu b=0 thì a000 – a0 = aa00 (sai)
Nếu b=5 thì
__ a500
__a5___
aa55
a=4
c) thay a=7/6 b=6/5 thi 3 x a + 4 : b - 5/12=3.7/6+4.6/5-5/12=7/2+24/5-5/12=210/60+288/60-25/60=473/60
**** nha
15 tháng 5 2015
\(\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}=\frac{\left(2.3.4.5.6\right).\left(3.4.5.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{7}{12}\)