Tìm n biết :
3^n - 3^n + 5.3^n-1 = 162 (3^n - 1 = 1/3)
Tìm n thuộc N biết :
a,32-n.16n=1024
b,3n-1+5.3n-1=162
3^-1.3^n+5.3^n-1=162
\(3^{-1}.3^n+5.3^{n-1}=162\)
\(3^{n-1}+5.3^{n-1}=162\)
\(3^{n-1}\left(5+1\right)=162\)
\(6.3^{n-1}=162\)
\(3^{n-1}=27=3^3\)
=> \(n-1=3\)
\(n=4\)
vậy n=4
Tìm x thuộc N biết
\(5^n+5^{n+2}=650\)
\(32^{-n}.16^n=1024\)
\(3^{-1}.3^n+5.3^{n-1}=162\)
Ai nhanh tik
a, 5n+5n+2=650
=>5n+5n.52=650
=>5n(1+25)=650
=>5n.26=650
=>5n=25
=>5n=52
=>n=2
Vậy n=2
Tìm n thuộc N biết :
a, 2008n = 1
b, 5n + 5n+2 = 650
c, 2n = 1024
d, 3n-1 5.3n-1 = 162
\(2008^n=1\Rightarrow n=0\)
\(2^n=1024\Rightarrow2^n=2^{10}\Rightarrow n=10\)
tíc mình nha
\(a,2008^n=1=>n=0.\)
\(b,5^n+5^{n+2}=650\)
\(=>5^n\left(1+5^2\right)=650\)
\(=>5^n.26=650\)
\(=>5^n=650:26\)
tự tính tiếp nhé !!
\(c,2^n=1024=2^{10}=>n=10\)
\(d,3^{n-1}5.3^{n-1}=162\)mình nghĩ đề thiếu !
Ừ ! Mình xem lại đề bài rồi. Câu d, phải là 3n-1 + 5.3n-1 = 162
tìm n biết:
a,\(\left(\frac{1}{3}\right)^n.27^n=3^n\)
b,\(\frac{1}{2}.2^n+4.2^n=3^2.2^5\)
c,\(\frac{64}{\left(-2\right)^n}=-32\)
d,\(6^{3-n}=216\)
e,\(5^n+5^{n+2}=650\)
f,\(3^{n-1}+5.3^{n-1}=162\)
a)
\(\left(\frac{1}{3}\right)^n\cdot27^n=3^n\)
\(\Rightarrow\left(\frac{1}{3}\cdot27\right)^n=3^n\)
\(\Rightarrow9^n=3^n\)
\(\Rightarrow\left(3^2\right)^n=3^n\)
\(\Rightarrow3^{2n}=3^n\)
\(\Rightarrow2n=n\)
\(\Leftrightarrow n=0\)
Vậy \(n=0\)
d) Ta có:
\(6^{3-n}=216\)
\(\Rightarrow6^{3-n}=6^3\)
\(\Rightarrow3-n=3\)
\(\Rightarrow n=3-3\)
\(\Rightarrow n=0\)
Vậy \(n=0\)\(\text{ }\)
e) Ta có:
\(5^n+5^{n+2}=650\)
\(\Rightarrow5^n+5^n\cdot5^2=650\)
\(\Rightarrow5^n\cdot\left(1+5^2\right)=650\)
\(\Rightarrow5^n\cdot26=25\cdot26\)
\(\Rightarrow5^n=25\)
\(\Rightarrow5^n=5^2\)
\(\Rightarrow n=2\)
Vậy \(n=2\)
Tìm x
3 mũ -1 . 3 mũ x =5.3 mũ x-1 = 162
X €N
Tìm số tự nhiên n biết:
a) \(3^{n+1}+5.3^{n-2}=2592\)
b) \(3^{n+2}+5.3^{n-1}=864\)
Tìm x,y
a) \(\left(x-5\right)^2=\left(1-3x\right)^2\)
b)\(\left(3x-1\right)^{100}+\left(2y+1\right)^{200}\le0\)
Tìm n
\(\frac{1}{3}.3^n+5.3^{n-1}=162\)
\(\frac{1}{3}.3^n+5.3^{n-1}=162\)
<=> \(3^{n-1}+5.3^{n-1}=162\)
<=> \(3^{n-1}\left(1+5\right)=162\)
<=> \(3^{n-1}.6=162\)
<=> \(3^{n-1}=162:6\)
<=> \(3^{n-1}=27\)
<=> \(3^{n-1}=3^3\)
<=> n - 1 = 3
<=> n = 3 + 1 = 4
Câu 1
a) Từ gt=>\(\hept{\begin{cases}x-5=1-3x\\x-5=3x-1\end{cases}}\)
<=>\(\hept{\begin{cases}4x=6\\2x=-4\end{cases}}\)
<=>\(\hept{\begin{cases}x=\frac{3}{2}\\x=-2\end{cases}}\)
b) Ta có: \(\hept{\begin{cases}\left(3x-1\right)^{100}\ge0,\forall x\in R\\\left(2y+1\right)^{200}\ge0,\forall x\in R\end{cases}}\)
Kết hợp với đề bài => \(\hept{\begin{cases}3x-1=0\\2y+1=0\end{cases}}\)
=>\(\hept{\begin{cases}x=\frac{1}{3}\\y=-\frac{1}{2}\end{cases}}\)
Bài 2
\(\frac{1}{3}.3^n+5.3^{n-1}=162\)
<=>\(3^{n-1}+5.3^{n-1}=162\)
<=>\(6.3^{n-1}=162\)
<=>\(3^{n-1}=27=3^3\)
<=>\(n-1=3\)
<=>\(n=4\)
b, Dấu = khi \(\hept{\begin{cases}x=\frac{1}{3}\\y=-\frac{1}{2}\end{cases}}\)
\(pt< =>6.3^{n-1}=162< =>3^{n-1}=3^3< =>n=4\)
tìm x thuộc N
5x+5x+2=605
3x-1+5.3x-1=162
3x-1+5.3x-1=162
=>3x-1.6=162
=>3x-1=162:6
=>3x-1=27=33
=>x-1=3
=>x=4