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H9
HT.Phong (9A5)
CTVHS
18 tháng 7 2023
1) \(3^x=\dfrac{9^8}{27^3\cdot81^2}\)
\(\Rightarrow3^x=\dfrac{\left(3^2\right)^8}{\left(3^3\right)^3\cdot\left(3^4\right)^2}\)
\(\Rightarrow3^x=\dfrac{3^{16}}{3^{15}}\)
\(\Rightarrow3^x=3\)
\(\Rightarrow x=1\)
2) \(\dfrac{2^{4-x}}{16^5}=32^6\)
\(\Rightarrow\dfrac{2^{4-x}}{\left(2^4\right)^5}=\left(2^5\right)^6\)
\(\Rightarrow\dfrac{2^{4-x}}{2^{20}}=2^{30}\)
\(\Rightarrow2^{4-x}=2^{20}\cdot2^{30}\)
\(\Rightarrow2^{4-x}=2^{50}\)
\(\Rightarrow4-x=50\)
\(\Rightarrow x=-46\)
3) \(\dfrac{2^{2x-3}}{4^{10}}=8^3\cdot16^5\)
\(\Rightarrow\dfrac{2^{2x-3}}{\left(2^2\right)^{10}}=\left(2^3\right)^3\cdot\left(2^4\right)^5\)
\(\Rightarrow\dfrac{2^{2x-3}}{2^{20}}=2^{29}\)
\(\Rightarrow2^{2x-3}=2^{49}\)
\(\Rightarrow2x-3=49\)
\(\Rightarrow2x=52\)
\(\Rightarrow x=26\)
LK
2
17 tháng 9 2019
a, \(27< 3^x< 3\cdot81\)
=> \(3^3< 3^x< 3\cdot3^4\)
=> \(3^3< 3^x< 3^5\)
=> x = 4
b, \(4^{15}\cdot9^{15}< 2^x\cdot3^x< 18^{16}\cdot216\)
=> \(\left[2^2\right]^{15}\cdot\left[3^2\right]^{15}< 2^x\cdot3^x< \left[2\cdot3^2\right]^{16}\cdot6^3\)
=> \(2^{30}\cdot3^{30}< 2^x\cdot3^x< 2^{16}\cdot3^{32}\cdot2^3\cdot3^3\)
=> \(2^{30}\cdot3^{30}< 2^x\cdot3^x< 2^{19}\cdot3^{35}\)
Đến đây tìm được x
\(c,2^{x+1}\cdot3^y=2^{2x}\cdot3^x\Leftrightarrow\frac{2^{2x}}{2^{x+1}}=\frac{3^y}{3^x}\Leftrightarrow2^{x-1}=3^{y-x}\)
\(\Leftrightarrow x-1=y-x=0\Leftrightarrow x=1\)
\(d,6^x:2^{2000}=3^y\)
=> \(\frac{6^x}{3^y}=2^{2000}\)
=> \(\frac{3^{2x}}{3^y}=2^{2000}\)
=> \(3^{2x-y}=2^{2000}\)
Đến đây tìm thử x,y
LN
21 tháng 9 2017
\(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Rightarrow\left(2x-1\right)^8-\left(2x-1\right)^6=0\)
\(\Rightarrow\left(2x-1\right)^6\left[\left(2x-1\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x-1\right)^6=0\\\left(2x-1\right)^2-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=0\\\left[{}\begin{matrix}2x-1=1\\2x-1=-1\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=1\\\left[{}\begin{matrix}2x=2\\2x=0\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\\left[{}\begin{matrix}x=1\\x=0\end{matrix}\right.\end{matrix}\right.\)
NT
0
ND
Nguyễn Đức Trí
VIP
27 tháng 7 2023
Bài 6 :
a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)
b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)
c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)
d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)
ND
Nguyễn Đức Trí
VIP
27 tháng 7 2023
Bài 7 :
a) \(3^x+3^{x+2}=9^{17}+27^{12}\)
\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)
\(\Rightarrow10.3^x=3^{34}+3^{36}\)
\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)
\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)
b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)
\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)
\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)
c) Bài C bạn xem lại đề
d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)
\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)
\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)
\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)
\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)
\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)
NH
0