tìm x biết
\(5^{x+1}-2\cdot5^x=375\)
\(9^{x+1}-5\cdot3^{2x}=324\)
\(\left(1-x\right)^5=32\)
\(3\cdot5^{2x+1}-3\cdot25^x=300\)
help me !!! mình đang cần luôn giải hộ mình với
TÌM X HỘ MIK NHA MÌNH CẢM ƠN\(\left(X+\frac{1}{1\cdot3}\right)+\left(X+\frac{1}{3\cdot5}\right)+...+\left(X+\frac{1}{23\cdot25}\right)=11\cdot X+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{242}\right)\)
\(\left(X+\frac{1}{1.3}\right)+\left(X+\frac{1}{3.5}\right)+...+\left(X+\frac{1}{23.25}\right)=11.X+\)\(\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)\)
\(\Leftrightarrow12X+\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{23.25}\right)+11X\)\(+\frac{\left(1+\frac{1}{3}+...+\frac{1}{81}\right)-\left(\frac{1}{3}+\frac{1}{9}+...+\frac{1}{243}\right)}{2}\)
\(\Leftrightarrow X+\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{23}+\frac{1}{23}-\frac{1}{25}\right)=\frac{242}{243}:2\)
\(\Leftrightarrow X+\frac{12}{25}=\frac{121}{243}\)
\(\Leftrightarrow X=\frac{109}{6075}\)
Vậy X=109/6075
Chắc Sai kết quả chứ công thức đúng nha!!!...
Fighting!!!...
Đặt:
\(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{23.25}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{23.25}=\frac{3-1}{1.3}+\frac{5-3}{3.5}+...+\frac{25-23}{23.25}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{23}-\frac{1}{25}=1-\frac{1}{25}=\frac{24}{25}\)
=> \(A=\frac{12}{25}\)
Đặt \(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\)
\(3B=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\)
=> \(3B-B=\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+\frac{1}{3^5}\right)=1-\frac{1}{3^5}=\frac{242}{243}\)
=> \(2B=\frac{242}{243}\Rightarrow B=\frac{121}{243}\)
Giải phương trình:
\(\left(x+\frac{1}{1.3}\right)+\left(x+\frac{1}{3.5}\right)+...+\left(x+\frac{1}{23.25}\right)=11x+\left(\frac{1}{3}+\frac{1}{9}+...+\frac{1}{243}\right)\)
\(12x+\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{23.25}\right)=11x+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{242}\right)\)
\(12x+\frac{12}{25}=11x+\frac{121}{243}\)
\(12x-11x=\frac{121}{243}-\frac{12}{25}\)
\(x=\frac{109}{6075}\)
1. Tìm x
a) \(2^x+5=21\)
b) \(2^x-1+3^2=5^2+2\cdot5\)
c) \(\left(2x-1\right)^3+5=130\)
d) \(5^{2x-3}-2\cdot5^2=5^2\)
e) \(3^{2x+1}-2=3^2+\left[5^2-3\left(2^2-1\right)\right]\)
f) \(\left(7^x-11\right)^3=2^5\cdot5^2+200\)
g) \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
a) \(2^x+5=21\)
\(\Rightarrow2^x=21-5=16\Rightarrow2^x=2^4\)
Vậy x = 4
b) \(2^x-1+3^2=5^2+2.5\)
\(\Rightarrow2^x-1+9=35\)
\(\Rightarrow2^x=35-9+1=27\)
Vậy x không có giá trị
c;d;e;f làm tương tự
Tìm \(x\)sao cho:
\(\left(x+\frac{1}{1\cdot3}\right)+\left(x+\frac{1}{3\cdot5}\right)+\left(x+\frac{1}{5\cdot7}\right)+...+\left(x+\frac{1}{23\cdot25}\right)=11\cdot x+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)\)
Chỉ biết \(x\) = \(\frac{109}{6075}\) thôi
Tìm x: a,\(\frac{x-1}{2011}+\frac{x-2}{2010}-\frac{x-3}{2009}=\frac{x-4}{2008}\)
b,\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{\left(2x-1\right)\left(2x+1\right)}=\frac{49}{99}\)
a, Ta có \(\frac{x-1}{2011}+\frac{x-2}{2010}-\frac{x-3}{2009}=\frac{x-4}{2008}\)
<=> \(\frac{x-1}{2011}+\frac{x-2}{2010}-\frac{x-3}{2009}-\frac{x-4}{2008}=0\)
<=> \(\left(\frac{x-1}{2011}-1\right)+\left(\frac{x-2}{2010}-1\right)-\left(\frac{x-3}{2009}-1\right)-\left(\frac{x-4}{2008}-1\right)=0\)
<=>\(\frac{x-2012}{2011}+\frac{x-2012}{2010}-\frac{x-2012}{2009}-\frac{x-2012}{2008}=0\)
<=> \(\left(x-2012\right)\left(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\right)=0\)
Mà \(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\ne0\)
=> \(x-2012=0=>x=2012\)
b, \(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{\left(2x-1\right)\left(2x+1\right)}=\frac{49}{99}\)
=>\(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{\left(2x-1\right)\left(2x+1\right)}=2\cdot\frac{49}{99}\)
=>\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2x-1}-\frac{1}{2x+1}=\frac{98}{99}\)
=>\(1-\frac{1}{2x+1}=\frac{98}{99}\)
=>\(\frac{2x}{2x+1}=\frac{98}{99}\)
=>2x = 98
=>x = 49
1. Tìm x
a) \(2^x+5=21\)
b) \(2^x-1+3^2=5^2+2\cdot5\)
c) \(\left(2x-1\right)^3+5=130\)
d) \(5^{2x-3}-2\cdot5^2=5^2\)
e) \(3^{2x+1}-2=3^2+\left[5^2-3\left(2^2-1\right)\right]\)
f) \(\left(7x-11\right)^3=2^5\cdot5^2+200\)
g) \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
Giúp với nha
a) \(2^x+5=21\)
\(2^x=21-5\)
\(2^x=16\)
\(2^x=2^4\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
a ) \(2^x+5=21\)
\(2^x=21-5\)
\(2^x=16\)
\(2^x=2^4\)
\(\Rightarrow x=4\)
Tìm x:
1) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
2) \(2\cdot3^x=10\cdot3^{12}+8\cdot27^4\)
3) \(\left(19x+2\cdot5^2\right):14=\left(13-8\right)^2-4^2\)
1) ( 2x -15 )5 = ( 2x - 15 )3
( 2x -15 )5 - ( 2x - 15 )3 = 0
( 2x - 15 )3 . [ ( 2x - 15 )2 - 1 ] = 0
\(\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)
\(\orbr{\begin{cases}2x-15=0\\2x-15=1\end{cases}}\)
\(\orbr{\begin{cases}2x=15\\2x=16\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{15}{2}\\x=8\end{cases}}\)
Tìm x:
a,\(15-\left(5-2x\right)=-4\)
b,\(\left|x-3\right|+1=4\)
c,\(5^x\cdot5^{x+1}\cdot5^{x+2}=10000000\div2^{18}\)
a.15-(5-2x)=-4
\(\Leftrightarrow\)15-5+2x=-4
\(\Leftrightarrow\)2x=-4-15+5
\(\Leftrightarrow\)2x=-14
\(\Leftrightarrow\)x=-7
b.TH1:x-3\(\ge\)0 \(\Rightarrow\)x\(\ge\)3
Ta có \(|\)x-3\(|\)=x-3
PT trên\(\Leftrightarrow\)x-3+1=4
\(\Leftrightarrow\)x=4+3-1
\(\Leftrightarrow\)x=6(nhận)
TH2:x-3<0\(\Leftrightarrow\)x<3
Ta có:\(|\)x-3\(|\)=-x+3
PT trên\(\Leftrightarrow\)-x+3+1=4
-x=4-3-1
x=0(nhận)
Vậy S={0;6}
chỗ 100000 là 1000000000000000000.mười tám chữ số 0
tìm x biết:
a) 3/2x+1/ - 2/5-x/=1
b)/2-3x/ -3/5-3x/=x-1
Giải hộ mình với mình cần gấp
help!
Giải phương trình :\(\left(\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+......+\frac{3}{97\cdot99}\right)\left(2x+1\right)=x+\frac{1}{33}\)
\(\left(\frac{3}{1.3}+\frac{3}{3.5}+.......+\frac{3}{97.99}\right).\left(2x+1\right)=x+\frac{1}{33}\)
\(\Rightarrow[\frac{3}{2}.(\frac{2}{1.3}+\frac{2}{3.5}+.......+\frac{2}{97.99})].\left(2x+1\right)=x+\frac{1}{33}\)
\(\Rightarrow[\frac{3}{2}.(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+......+\frac{1}{97}-\frac{1}{99})].\left(2x+1\right)=x+\frac{1}{33}\)
\(\Rightarrow[\frac{3}{2}.(1-\frac{1}{99})].\left(2x+1\right)=x+\frac{1}{33}\)
\(\Rightarrow\left(\frac{3}{2}.\frac{98}{99}\right).\left(2x+1\right)=x+\frac{1}{33}\)
\(\Rightarrow\frac{49}{33}.\left(2x+1\right)=x+\frac{1}{33}\)
\(\Rightarrow\frac{49}{33}.2x+\frac{49}{33}=x+\frac{1}{33}\)
\(\Rightarrow\frac{98}{33}.x+\frac{49}{33}=x+\frac{1}{33}\)
\(\Rightarrow\frac{98}{33}.x-x=\frac{1}{33}-\frac{49}{33}\)
\(\Rightarrow\frac{65}{33}.x=\frac{-16}{11}\)
\(\Rightarrow x=\frac{-16}{11}:\frac{65}{33}\)
\(\Rightarrow x=\frac{-48}{65}\)
Vậy \(x=\frac{-48}{65}\)