Tìm x ∈ N biết :
a) \(8< 2^x\le2^9.2^{-5}\)
b)\(27< 81^3:3^x< 243\)
c)\(\left(\dfrac{2}{5}\right)^x>\left(\dfrac{5}{2}\right)^{-3}.\left(\dfrac{-3}{5}\right)^2\)
Tìm x:
\(a\)) \(\dfrac{2}{3}+\left(x-\dfrac{1}{2}\right)^3=\dfrac{19}{27}\)
\(b\)) \(\left(\dfrac{3}{2}\right)^{2x-1}:\left(\dfrac{27}{8}\right)^3=\dfrac{81}{16}\)
\(c\)) \(\dfrac{1}{2}.2^x+4.2^x=9.2^5\)
\(d\)) \(\text{12 - (2x +1)}^2=-69\)
\(a,\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}=\left(\dfrac{1}{3}\right)^3\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{1}{3}\Rightarrow x=\dfrac{5}{6}\\ b,\Rightarrow\left(\dfrac{3}{2}\right)^{2x-1}:\left(\dfrac{3}{2}\right)^9=\left(\dfrac{3}{2}\right)^4\\ \Rightarrow2x-1-9=4\\ \Rightarrow2x=14\Rightarrow x=7\\ c,\Rightarrow2^{x-1}+2^{x+2}=9\cdot2^5\\ \Rightarrow2^{x-1}\left(1+2^3\right)=9\cdot2^5\\ \Rightarrow2^{x-1}\cdot9=9\cdot2^5\\ \Rightarrow2^{x-1}=2^5\Rightarrow x-1=5\Rightarrow x=6\\ d,\Rightarrow\left(2x+1\right)^2=12+69=81\\ \Rightarrow\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)
\(a,\dfrac{2}{3}+\left(x-\dfrac{1}{2}\right)^3=\dfrac{19}{27}\)
\(\left(x-\dfrac{1}{2}\right)^3=\dfrac{19}{27}-\dfrac{2}{3}\)
\(\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\left(\dfrac{1}{3}\right)^3\)
\(\Rightarrow x-\dfrac{1}{2}=\dfrac{1}{3}\)
\(x=\dfrac{1}{2}+\dfrac{1}{3}\)
\(x=\dfrac{1}{5}\)
Tìm x \(\in\) N biết :
a)\(8< 2^x\le2^9.2^{-5}\)
b) \(27< 81^3:3^x< 243\)
c)\(\left(\frac{2}{5}\right)^x>\left(\frac{5}{2}\right)^{-3}.\left(\frac{-2}{5}\right)^2\)
a,\(8< 2^x\le2^9.2^{-5}\)
\(2^3< 2^x\le2^4\)
\(\Rightarrow x=4\)
b, \(27< 81^3.3^x< 243\)
\(3^3< 3^{12-x}< 3^5\)
\(\Rightarrow3< 12-x< 5\)
12-x=4
x=8
c,\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^3.\left(\frac{2}{5}\right)^2\)
\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^5\)
\(\Rightarrow x>5\)
x=6;7;8........
1.
a, \(^{^2}\left(x-2\right)=9\) b,\(^{^3}\left(3x-1\right)=-8\) c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\) d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\) e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\) f,\(\left(\dfrac{1}{2}\right)^{2x-1}=8\)
2.tìm số tự nhiên n biết
a, \(3^{n-1}=27\) b, \(3^{n-1}=\dfrac{1}{243}\) c, \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\) d, \(\left(-\dfrac{1}{3}\right)^{n-5}=\dfrac{1}{81}\) e,\(2^{-1}.2^n+4.2^n=9.2^5\)
Bài 1:
a, \(\left(x-2\right)^2=9\)
\(\Rightarrow x-2\in\left\{-3;3\right\}\Rightarrow x\in\left\{-1;5\right\}\)
b, \(\left(3x-1\right)^3=-8\)
\(\Rightarrow3x-1=-2\Rightarrow3x=-1\)
\(\Rightarrow x=-\dfrac{1}{3}\)
c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
\(\Rightarrow x+\dfrac{1}{2}\in\left\{-\dfrac{1}{4};\dfrac{1}{4}\right\}\)
\(\Rightarrow x\in\left\{-\dfrac{3}{4};-\dfrac{1}{4}\right\}\)
d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^2\)
Vì \(\dfrac{2}{3}\ne\pm1;\dfrac{2}{3}\ne0\) nên \(x=2\)
e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{x-1}=\left(\dfrac{1}{2}\right)^4\)
Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(x-1=4\Rightarrow x=5\)
f, \(\left(\dfrac{1}{2}\right)^{2x-1}=8\) \(\Rightarrow\left(\dfrac{1}{2}\right)^{2x-1}=\left(\dfrac{1}{2}\right)^{-3}\) Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(2x-1=-3\) \(\Rightarrow2x=-2\Rightarrow x=-1\) Chúc bạn học tốt!!!tìm x biết:
a) \(5^x.\left(5^3\right)^2=625\)
b)\(\left(\dfrac{12}{15}\right)^x=\left(\dfrac{5}{3}\right)^{-5}-\left(-\dfrac{3}{5}\right)^4\)
c)\(\left(-\dfrac{3}{4}\right)^{3x-1}=\dfrac{256}{81}\)
d)\(172x^2-7^9:98^3=2^{-3}\)
Tìm \(x\) biết:
\(\left(\sqrt{3}\right)^x=243\)
\(0,1^x=1000\)
\(\left(\dfrac{1}{2}\right)^x=1024\)
\(\left(0,2\right)^{x+3}< \dfrac{1}{5}\)
\(\left(\dfrac{3}{5}\right)^{2x+1}>\left(\dfrac{5}{3}\right)^2\)
\(5^{x-1}+5^{x+2}=3\)
a: \(\left(\sqrt{3}\right)^x=243\)
=>\(3^{\dfrac{1}{2}\cdot x}=3^5\)
=>\(\dfrac{1}{2}\cdot x=5\)
=>x=10
b: \(0,1^x=1000\)
=>\(\left(\dfrac{1}{10}\right)^x=1000\)
=>\(10^{-x}=10^3\)
=>-x=3
=>x=-3
c: \(\left(0,2\right)^{x+3}< \dfrac{1}{5}\)
=>\(\left(0,2\right)^{x+3}< 0,2\)
=>x+3>1
=>x>-2
d: \(\left(\dfrac{3}{5}\right)^{2x+1}>\left(\dfrac{5}{3}\right)^2\)
=>\(\left(\dfrac{3}{5}\right)^{2x+1}>\left(\dfrac{3}{5}\right)^{-2}\)
=>2x+1<-2
=>2x<-3
=>\(x< -\dfrac{3}{2}\)
e: \(5^{x-1}+5^{x+2}=3\)
=>\(5^x\cdot\dfrac{1}{5}+5^x\cdot25=3\)
=>\(5^x=\dfrac{3}{25,2}=\dfrac{1}{8,4}=\dfrac{10}{84}=\dfrac{5}{42}\)
=>\(x=log_5\left(\dfrac{5}{42}\right)=1-log_542\)
Tìm x biết:
a) \(\dfrac{-32}{\left(-2\right)^x}=4\) f) \(\left(3x-1\right)^3=\dfrac{-8}{27}\)
b) \(\left(\dfrac{1}{2}\right)^{2x-1}=\dfrac{1}{8}\) g) \(\left(2x+3\right)^2=\dfrac{9}{121}\)
c) \(\dfrac{1}{9}.27^x=3^x\) h) \(5^x+5^{x+2}=650\)
d) \(9^x:3^3=\dfrac{1}{243}\) i) \(\left(x-7\right)^{x+1}-\left(x-7\right)=0\)
e) \(\dfrac{x7}{81}=27\) m) \(\left(\dfrac{-3}{4}\right)^{3x-1}=\dfrac{256}{81}\)
h) \(5^x+5^{x+2}=650\)
\(\Leftrightarrow5^x+5^x.5^2=650\)
\(\Leftrightarrow5^x\left(1+25\right)=650\)
\(\Leftrightarrow5^x.26=650\)
\(\Leftrightarrow5^x=25\)
\(\Leftrightarrow x=2\)
haizzz,đăng ít thôi,chứ nhìn hoa mắt quá =.=
tìm x:
\(a,5^x.\left(5^2\right)^3=625\)
\(b,\left(\dfrac{12}{15}\right)^x=\left(\dfrac{5}{4}\right)^{-2}-\left(\dfrac{-3}{5}\right)^4\)
\(c,\left(\dfrac{-3}{4}\right)^{3x-1}=\dfrac{256}{81}\)
\(d,172x^2-7^9:98^3=2^{-3}\)
giải phương trình
a) \(5^x=4\)
b) \(5^{2-x}=8\)
c) \(\left(\dfrac{1}{3}\right)^{4+x}=243\)
d) \(\left(\dfrac{2}{3}\right)^x=\dfrac{3}{2}\)
a: \(5^x=4\)
=>\(x=log_54\)
b: \(5^{2-x}=8\)
=>\(2-x=log_58\)
=>\(x=2-log_58\)
c: \(\left(\dfrac{1}{3}\right)^{x+4}=243\)
=>\(3^{-x-4}=3^5\)
=>-x-4=5
=>-x=9
=>x=-9
d: \(\left(\dfrac{2}{3}\right)^x=\dfrac{3}{2}\)
=>\(\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^{-1}\)
=>x=-1
Tìm x biết:
a) \(\left(-\dfrac{2}{3}\right)^2.x=\left(-\dfrac{2}{3}\right)^5\) ; b) \(\left(-\dfrac{1}{3}\right)^3.x=\dfrac{1}{81}\) ; c) (2x-3)\(^2\) ; d) (3x-2)\(^5\) =-243
a: =>x=(-2/3)^5:(-2/3)^2=(-2/3)^3=-8/27
b: =>x*(-1/3)^3=(-1/3)^4
=>x=-1/3
d: =>3x-2=-3
=>3x=-1
=>x=-1/3