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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
\(=\)\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{2^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{3^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{5^3}\right)\)\(...\) \(\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\) \(\left(\frac{1}{125}-\frac{1}{1^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{2^3}\right)\) \(.\) \(\left(\frac{1}{125}-\frac{1}{3^3}\right)\) \(.\) \(0\) \(....\) \(\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\) \(0\)
\(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}< =>\left(x-\frac{2}{15}\right)^3=\left(\frac{2}{5}\right)^3\)
=> \(x-\frac{2}{15}=\frac{2}{5}\)
x = \(\frac{8}{15}\)
(x-2/15)^3=8/125
(x-2/15)^3=(2/5)^3
(x-2/15)=2/5
x=2/5+2/15
x=8/15
vậy x=8/15
Ta có \(M=\frac{1}{125\cdot2^3}\cdot\frac{1}{125\cdot3^3}\cdot\frac{1}{125\cdot4^3}\cdot...\cdot\frac{1}{125\cdot20^3}\)
\(\Rightarrow M=0\)
\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...0...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=0\)
\(\frac{x}{6}=\frac{8}{3}\Leftrightarrow x=\frac{6.8}{3}=16\)
\(\frac{125}{x}=\frac{25}{3}\Leftrightarrow x=\frac{125.3}{25}=15\)
\(\frac{0,1}{5}=\frac{2,1}{x}\Leftrightarrow x=\frac{5.2,1}{0,1}=105\)
\(\frac{x-2}{3}=\frac{4}{5}\Leftrightarrow x-2=\frac{12}{5};x=\frac{22}{5}\)