a) \(\left(3^x-5\right)^4=2^8\)

\(\Rightarrow\left(3^x-5\right)^4=\left(2^2\right)^4\)

\(\Rightarrow\left(3^x-5\right)^4=4^4\)

\(\Rightarrow3^x-5=4\)

\(\Rightarrow3^x=4+5\)

\(\Rightarrow3^x=9\)

\(\Rightarrow3^x=3^3\)

\(\Rightarrow x=3\)

Vậy \(x=3\).

b) \(3^{x+2}+3^x=10^2-10\)

\(\Rightarrow3^x\left(3^2+1\right)=10\left(10-1\right)\)

\(\Rightarrow3^x\cdot10=90\)

\(\Rightarrow3^x=\dfrac{90}{10}=9\)

\(\Rightarrow3^x=3^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\).

c) \(3^{x+1}-3^x=4\cdot5-2\)

\(\Rightarrow3^x\left(3-1\right)=20-2\)

\(\Rightarrow3^x\cdot2=18\)

\(\Rightarrow3^x=\dfrac{18}{2}=9\)

\(\Rightarrow3^x=3^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\).

d) \(5^{x+2}-5^x=10^3:2+10^2\)

\(\Rightarrow5^x\left(5^2-1\right)=1000:2+100\)

\(\Rightarrow5^x\cdot24=600\)

\(\Rightarrow5^x=\dfrac{600}{24}=25\)

\(\Rightarrow5^x=5^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\).

e) \(4^x+4^{x-1}=84:7\)

\(\Rightarrow4^x:1+4^x:4=12\)

\(\Rightarrow4^x\cdot1+4^x\cdot\dfrac{1}{4}=12\)

\(\Rightarrow4^x\left(1+\dfrac{1}{4}\right)=12\)

\(\Rightarrow4^x\cdot\dfrac{5}{4}=12\)

\(\Rightarrow4^x=12:\dfrac{5}{4}=12\cdot\dfrac{4}{5}=9.6\)

\(\Rightarrow x\in\left\{\varnothing\right\}\)

Vậy \(x\in\left\{\varnothing\right\}\).

a) \(\overline{ab}\)

b) \(\overline{abc}\)

c) \(\overline{aabb}\)

\(\left|\dfrac{2}{5}\right|-\left|-0,2\right|\cdot\left|-7\right|\)

\(=\dfrac{2}{5}-0,2\cdot7\)

\(=\dfrac{2}{5}-\dfrac{7}{5}\)

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

\(3^x=81\\ 3^x=3^4\\ x=4\)

Vậy \(x=4.\)

a) \(\left(x-2\right)\left(2y+1\right)=8\)

Ta lập bảng sau:

Vậy các cặp số nguyên \(\left(x;y\right)\) là: \(\left(10;0\right);\left(-6;-1\right)\).

b) \(\left(8-x\right)\left(4y+1\right)=20\)

Ta lập bảng sau:

Vậy các cặp số nguyên \(\left(x;y\right)\) là: \(\left(4;1\right);\left(-12;0\right)\).