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\(\dfrac{4^3.5^4}{10^3.2^3}=\dfrac{2^6.5^4}{5^3.2^3.2^3}=\dfrac{2^6.5^4}{5^3.2^6}=5\)
a) Ta có: \(3\cdot5^x=3\cdot5^4\)
\(\Leftrightarrow5^x=5^4\)
\(\Leftrightarrow x=4\)
Vậy: x=4
b) Ta có: \(9\cdot7^x=6\cdot7^5+3\cdot7^5\)
\(\Leftrightarrow9\cdot7^x=\left(6+3\right)\cdot7^5\)
\(\Leftrightarrow9\cdot7^x=9\cdot7^5\)
\(\Leftrightarrow7^x=7^5\)
\(\Leftrightarrow x=5\)
Vậy: x=5
c) Ta có: \(2\cdot3^{x+2}+4\cdot3^{x+1}=10\cdot3^7\)
\(\Leftrightarrow2\cdot3^{x+2}+2\cdot6^{x+1}=10\cdot3^7\)
\(\Leftrightarrow2\cdot\left(3^{x+2}+6^{x+1}\right)=10\cdot3^7\)
\(\Leftrightarrow3^{x+2}+6^{x+1}=\frac{10\cdot3^7}{2}\)
\(\Leftrightarrow3^{x+1}\cdot3+3^{x+1}\cdot2=5\cdot3^7\)
\(\Leftrightarrow3^{x+1}\cdot\left(3+2\right)=5\cdot3^7\)
\(\Leftrightarrow5\cdot3^{x+1}=5\cdot3^7\)
\(\Leftrightarrow3^{x+1}=3^7\)
\(\Leftrightarrow x+1=7\)
\(\Leftrightarrow x=6\)
Vậy: x=6
a) \(3.5^x=3.5^4\)
\(\Rightarrow3.5^x-3.5^4=0\)
\(\Rightarrow3.\left(5^x-5^4\right)=0\)
Vì \(3\ne0.\)
\(\Rightarrow5^x-5^4=0\)
\(\Rightarrow5^x=0+5^4\)
\(\Rightarrow5^x=5^4\)
\(\Rightarrow x=4\left(TM\right).\)
Vậy \(x=4.\)
Chúc bạn học tốt!
a,?????
b, Với mọi giá trị của x;y ta có:
\(\left|x-\dfrac{1}{2}\right|+\left|x+y\right|\ge0\)
Để \(\left|x-\dfrac{1}{2}\right|+\left|x+y\right|=0\) thì:
\(\left\{{}\begin{matrix}\left|x-\dfrac{1}{2}\right|=0\\\left|x+y\right|=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\\dfrac{1}{2}+y=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=-\dfrac{1}{2}\end{matrix}\right.\)
Vậy..........
c, \(\left|2x\right|-\left|3,5\right|=\left|-6,5\right|\)
\(\Rightarrow\left|2x\right|=6,5+3,5=10\)
\(\Rightarrow\left\{{}\begin{matrix}2x=10\\2x=-10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
Vậy..........
d, \(\left|x-1,7\right|=2,3\)
\(\Rightarrow\left\{{}\begin{matrix}x-1,7=2,3\\x-1,7=-2,3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=4\\x=-0,6\end{matrix}\right.\)
Vậy.........
Chúc bạn học tốt!!!
\(=\dfrac{5^6\cdot3^6\cdot\dfrac{1}{2}+5^8}{5^6\cdot26}=\dfrac{3^6\cdot\dfrac{1}{2}+5^2}{26}=\dfrac{779}{52}\)
\(\dfrac{2^2\cdot3^3\cdot5}{3\cdot2^3\cdot5^3}=\dfrac{1}{2}\cdot3^2\cdot\dfrac{1}{5^2}=\dfrac{1}{2}\cdot\dfrac{9}{25}=\dfrac{9}{50}\)