1.
a) \(5x.5x.5x=\left(5x\right)^3.\)
b) \(x^1.x^2.....x^{2006}=x^{\frac{\left(2006+1\right).2006}{2}=}x^{2013021}.\)
c) \(x^1.x^4.x^7.....x^{100}=x^{\frac{\left(100+1\right).\left(\frac{100-1}{3}+1\right)}{2}}=x^{1717}.\)
d) \(x^2.x^5.x^8.....x^{2003}=x^{\frac{\left(2003+2\right).\left(\frac{2003-2}{3}+1\right)}{2}}=x^{669670}.\)
2.
\(2^x+80=3^y\)
Với \(x>0\Rightarrow2^x\) chẵn
Và 80 chẵn
\(\Rightarrow2^x+80\) chẵn.
Mà \(3^y\) lẻ
\(\Rightarrow x< 0.\)
Mà \(x\in N\)
\(\Rightarrow x=0.\)
\(\Rightarrow2^0+80=3^y\)
\(\Rightarrow1+80=3^y\)
\(\Rightarrow3^y=81\)
\(\Rightarrow3^y=3^4\)
\(\Rightarrow y=4.\)
Vậy \(\left(x;y\right)=\left(0;4\right).\)
Chúc bạn học tốt!
1.viết tích dưới dạng lũy thừa
a.5x.5x.5x
=(5x)\(^3\)
b.x\(^1\) . x \(^2\).......x \(^{2006}\)
=x \(^{2013021}\)
c.x\(^1\).x \(^4\) .x \(^7\)......x \(^{100}\)
=x \(^{1717}\)
d.x \(^2\) .x \(^5\).x \(^8\).......x\(^{2003}\)
=x \(^{669670}\)
2 \(^x\)+80=3\(^y\)
ta có 3\(^y\)lẻ nên 2 \(^x\)+80 lẻ .
Với x \(\ge\)1
thì 2 \(^x\)+80 chẵn không thỏa mãn
nên x=0
=>1+80=3\(^y\)
=>81=3\(^y\)
=>3\(^4\)=3\(^y\)
=>y=4
