\(\left(x-\frac{3}{2}\right)^5=\frac{-125}{32}\)
a,\((\frac{32}{81})^2.\left(\frac{-9}{8}\right)^5.\left(-4\right)^3̣\)
b,\(\left(-25\right)^5:125^2:\left(-5\right)^3\)
c,\(\left(\frac{8}{27}\right)^3:\left(\frac{-2}{3}\right)^8\)
a)\(\left(1-\frac{2}{5}\right)^2+\left|\frac{-3}{5}\right|+\frac{-7}{10}\)
b)\(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}\)
c)\(\frac{\left(-5\right)^{32}.20^{43}}{\left(-8\right)^{29}.125^{25}}\)
tìm số nguyên x, biết:
a, \(\left(\frac{1}{5}\right)^x=\left(\frac{1}{125}\right)^3\)
b, \(\left(\frac{3}{5}\right)^x=\left(\frac{9}{25}\right)^3\)
c,\(2^{3-2x}=8^3\)
d, \(2^{3x+1}=32^2\)
e, \(3^{6-3x}=81^3\)
a/ \(\left(\frac{1}{5}\right)^x=\left(\frac{1}{5^3}\right)^3=\left(\frac{1}{5}\right)^9\Rightarrow x=9\)
b/ \(\left(\frac{3}{5}\right)^x=\left(\frac{3^2}{5^2}\right)^3=\left(\frac{3}{5}\right)^6\Rightarrow x=6\)
c\(2^{3-2x}=\left(2^3\right)^3=2^9\Rightarrow3-2x=9\Rightarrow x=-3\)
d/ \(2^{3x+1}=32^2=\left(2^5\right)^2=2^{10}\Rightarrow3x+1=10\Rightarrow x=3\)
e/ \(3^{6-3x}=81^3=\left(3^4\right)^3=3^{12}\Rightarrow6-3x=12\Rightarrow x=-2\)
\(\left(\frac{1}{5}\right)^x=\left(\frac{1}{125}\right)^3\Leftrightarrow\left(\frac{1}{5}\right)^x=\left[\left(\frac{1}{5}\right)^3\right]^3\Leftrightarrow\left(\frac{1}{5}\right)^x=\left(\frac{1}{5}\right)^9\Leftrightarrow x=9\)
\(\left(\frac{3}{5}\right)^x=\left(\frac{9}{25}\right)^3\Leftrightarrow\left(\frac{3}{5}\right)^x=\left[\left(\frac{3}{5}\right)^2\right]^3\Leftrightarrow\left(\frac{3}{5}\right)^x=\left(\frac{3}{5}\right)^6\Leftrightarrow x=6\)
\(2^{3-2x}=8^3\Leftrightarrow2^{3-2x}=\left(2^3\right)^3\Leftrightarrow2^{3-2x}=2^9\Leftrightarrow3-2x=9\)
\(\Leftrightarrow2x=3-9\Leftrightarrow2x=-6\Leftrightarrow x=\left(-6\right):2\Leftrightarrow x=-3\)
Các phép còn lại làm tương tự bn nha !
a)\(\left(\frac{1}{5}\right)^x=\left(\left(\frac{1}{5}\right)^3\right)^3=\left(\frac{1}{5}\right)^9\)
=>x=9
b)\(\left(\frac{3}{5}\right)^x=\left(\left(\frac{3}{5}\right)^2\right)^3=\left(\frac{3}{5}\right)^6\)
=>x=6
c) \(2^{3-2x}=\left(2^3\right)^3=2^9\)
=>3-2x=9
=>2x=-6
=>x=-3
d)\(2^{3x+1}=\left(2^5\right)^2=2^{10}\)
=>3x+1=10
=>x=3
e)\(3^{6-3x}=\left(3^4\right)^3=3^{12}\)
=>6-3x=12
=>3x=-6
=>x=-2
\(\left(4\frac{1}{6}x^2-\frac{2}{3}\right)\left(-0,75x-\frac{21}{32}\right)\left(\frac{5}{6}\left|x\right|-3\frac{1}{3}\right)\)\(\left(4\frac{1}{2}x^4+1\frac{1}{3}x\right)=0\)
\(\left(4\frac{1}{6}x^2-\frac{2}{3}\right)\left(-0,75x-\frac{21}{32}\right)\left(\frac{5}{6}\left|x\right|-3\frac{1}{3}\right)\)\(\left(4\frac{1}{2}x^4+1\frac{1}{3}x\right)=0\)
Tim x biet
k) \(\left[\left(3,75:\frac{1}{4}+2\frac{2}{5}.125\%\right)-\left(\frac{7}{2}.0,8-1,2:\frac{3}{2}\right)\right]:\left(1\frac{1}{2}+0,75\right)x=64\)
a)\(\left(\frac{1}{13}\right)^{13}:\left(\frac{1}{3}\right)^{x-2}=\frac{1}{81}\)
b)\(\left(0,4\right)^{x-1}:\left(\frac{2}{5}\right)^2=\frac{8}{125}\)
b) ( 2/5 )^ x-1 : ( 2/5 )^2 = ( 2/5 )^3
(2/5)^ x-1 = ( 2/5) ^3 . (2/5)^2
(2/5)^ x-1 = ( 2/5 ) ^ 6
=> x-1 = 6
=> x= 7
Tìm x, biết:
a) \(\left(\frac{-3}{4}\right)^{3x-1}=\frac{-27}{64}\)
b) \(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{265}\)
c) \(\frac{\left(x+3\right)^5}{\left(x+3\right)^2}=\frac{64}{27}\)
d) \(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
a) \(\left(-\frac{3}{4}\right)^{3x-1}=\frac{-27}{64}\)
\(\Leftrightarrow\left(-\frac{3}{4}\right)^{3x-1}=\left(-\frac{3}{4}\right)^3\)
\(\Leftrightarrow3x-1=3\)
\(\Leftrightarrow3x=4\)
\(\Leftrightarrow x=\frac{4}{3}\)
b) Đề sai ! Sửa :
\(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{625}\)
\(\Leftrightarrow\left(\frac{4}{5}\right)^{2x+5}=\left(\frac{4}{5}\right)^4\)
\(\Leftrightarrow2x+5=4\)
\(\Leftrightarrow2x=-1\)
\(\Leftrightarrow x=-\frac{1}{2}\)
c) \(\frac{\left(x+3\right)^5}{\left(x+5\right)^2}=\frac{64}{27}\)
\(\Leftrightarrow\left(x+3\right)^3=\left(\frac{4}{3}\right)^3\)
\(\Leftrightarrow x+3=\frac{4}{3}\)
\(\Leftrightarrow x=-\frac{5}{3}\)
d) \(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
\(\Leftrightarrow\left(x-\frac{2}{15}\right)^3=\left(\frac{2}{15}\right)^3\)
\(\Leftrightarrow x-\frac{2}{15}=\frac{2}{15}\)
\(\Leftrightarrow x=\frac{4}{15}\)
a) \(\frac{\left(-1\right)^3}{15}+\left(-\frac{2}{3}\right):2\frac{2}{3}-\left|-\frac{5}{6}\right|\)
b) \(1\frac{5}{13}-0,\left(3\right)-\left(1\frac{4}{9}+\frac{18}{13}-\frac{1}{3}\right)\)
c) \(\left|97\frac{2}{3}-125\frac{3}{5}\right|+97\frac{2}{5}-125\frac{1}{3}\)
d) \(\frac{2\cdot6^9-2^5\cdot18^4}{2^2\cdot6^8}\)