ta có : 

\(\frac{x+1}{3}+\frac{x+1}{9}+\frac{x+1}{27}+\frac{x+1}{81}=\left(x+1\right)\times\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)\)

\(=\left(x+1\right)\times\frac{40}{81}=\frac{56}{81}\text{ nên }x+1=\frac{56}{40}=\frac{7}{5}\)

vậy \(x=\frac{7}{5}-1=\frac{2}{5}\)

16/81

a)\(\left(\frac{3}{5}\right)^5\times x=\left(\frac{3}{7}\right)^7\)

\(\Leftrightarrow\frac{3^5}{5^5}\times x=\frac{3^7}{7^7}\)

\(\Leftrightarrow x=\frac{3^7}{7^7}:\frac{3^5}{5^5}\)

\(\Leftrightarrow x=\frac{3^7\times5^5}{7^7\times3^5}\)

\(\Leftrightarrow x=\frac{3^2\times5^5}{7^7}\)

b)\(\left(\frac{-1}{3}\right)^3\times x=\frac{1}{81}\)

\(\Leftrightarrow\frac{\left(-1\right)^3}{3^3}\times x=\frac{1}{3^4}\)

\(\Leftrightarrow x=\frac{1}{3^4}:\frac{-1}{3^3}\)

\(\Leftrightarrow x=\frac{1\times3^3}{3^4\times\left(-1\right)}\)

\(\Leftrightarrow x=\frac{1}{-3}\)

c)\(\Leftrightarrow\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)

\(\Leftrightarrow x-\frac{1}{2}=\frac{1}{3}\)

\(\Leftrightarrow x=\frac{1}{3}+\frac{1}{2}\)

\(\Leftrightarrow x=\frac{5}{6}\)

d)\(\Leftrightarrow\left(x+\frac{1}{2}\right)^4=\left(\frac{2}{3}\right)^4\)

\(\Leftrightarrow x+\frac{1}{2}=\frac{2}{3}\)

\(\Leftrightarrow x=\frac{2}{3}-\frac{1}{2}\)

\(\Leftrightarrow x=\frac{1}{6}\)

\(\frac{1}{\left(x-1\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+7\right)}+....+\frac{1}{\left(x+76\right).\left(x+80\right)}=-\frac{81}{320}\)

\(\Rightarrow\frac{4}{\left(x-1\right)\left(x+3\right)}+\frac{4}{\left(x+3\right)\left(x+7\right)}+...+\frac{4}{\left(x+76\right)\left(x+80\right)}=\frac{-81}{80}\)

\(\Rightarrow\frac{1}{x-1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+7}+...+\frac{1}{x+76}-\frac{1}{x+80}=\frac{-81}{80}\)

\(\Rightarrow\frac{1}{x-1}-\frac{1}{x+90}=\frac{-81}{80}\)

Vì \(\frac{-81}{80}< 0\Rightarrow\frac{1}{x-1}< \frac{1}{x+90}\)

\(\Leftrightarrow x-1>x+90\)( luôn sai \(\forall x\in R\))

Vậy không tìm được x 

tu hoc moi gioi

a, \(x=\dfrac{3}{4}-1=\dfrac{3}{4}-\dfrac{4}{4}=-\dfrac{1}{4}\)

b, \(x=\dfrac{1}{5}-4=\dfrac{1}{5}-\dfrac{20}{5}=-\dfrac{19}{5}\)

c, \(x=2+\dfrac{1}{5}=\dfrac{10}{5}+\dfrac{1}{5}=\dfrac{11}{5}\)

d, \(x=\dfrac{1}{81}-\dfrac{5}{3}=\dfrac{1}{81}-\dfrac{135}{81}=-\dfrac{134}{81}\)

\(a,\dfrac{3}{4}-x=1\\ \Rightarrow x=1,75\\ b,x+4=\dfrac{1}{5}\\ \Rightarrow x=-3,8\\ c,x-\dfrac{1}{5}=2\\ \Rightarrow x=2,2\\ d,x+\dfrac{5}{3}=\dfrac{1}{81}\\x=\dfrac{1}{81}-\dfrac{5}{3}\\ \Rightarrow x=-\dfrac{134}{81}\)

a) \(\dfrac{3}{4}-x=1\)

\(x=\dfrac{3}{4}-1\)

\(x=-\dfrac{1}{4}\)\(=0,25\)

b) \(x+4=\dfrac{1}{5}\)

\(x=\dfrac{1}{5}-4\)

\(x=-\dfrac{19}{5}\)\(=-3,8\)

c) \(x-\dfrac{1}{5}=2\)

\(x=2+\dfrac{1}{5}\)

\(x=\dfrac{11}{5}=2,2\)

d) \(x+\dfrac{5}{3}=\dfrac{1}{81}\)

\(x=\dfrac{1}{81}-\dfrac{5}{3}\)

\(x=-\dfrac{134}{81}\)

2*(4x+1)+3*(2x+3)=81

8x+2+6x+9=81

14x+11=81

14x=81-11

14x=70

x=70:14

x=5

a) \(3^{a+1}=81\)

\(3^{a+1}=3^4\)

\(a+1=4\)

\(a=3\)

b) \(\left(x-1\right)^3=27\)

\(\left(x-1\right)^3=3^3\)

\(x-1=3\)

\(x=4\)

\(a,3^{a+1}=81\\ \Rightarrow3^{a+1}=3^4\\ \\ \Rightarrow a+1=4\\ \Rightarrow a=3.\\ b,\left(x-1\right)^3=27\\ \Rightarrow\left(x-1\right)^3=3^3\\ \Rightarrow x-1=3\\ \Rightarrow x=4.\)