Bài 1 )
a ) \(2.2^2.2^3.....2^x=1024\Leftrightarrow2^{1+2+....+x}=2^{10}\Leftrightarrow1+2+....+x=10\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=10\Leftrightarrow\left(x+1\right)x=20=4.5\Rightarrow x=4\)
b ) \(\frac{37-x}{x+13}=\frac{3}{7}\Leftrightarrow3x+39=259-7x\Leftrightarrow3x+7x=259-39\Leftrightarrow10x=220\Rightarrow x=22\)
Bài 2 ) \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+\left(\frac{50^2-15.125}{5^4}\right)^{2014}=\frac{1}{2}.8-\frac{2}{5}+\left(\frac{5^4.2^2-3.5^4}{5^4}\right)^{2014}\)
\(=4-\frac{2}{5}+\left[\frac{5^4\left(4-3\right)}{5^4}\right]^{2014}=\frac{18}{5}+1=\frac{23}{5}\)
Mình làm bài 1 thui nha, còn bài 2 thì còn tự tính là được thôi mừ !!!
Bài 1:
a) \(2.2^2.2^3...2^x=1024\)
\(=>2^{1+2+3+...+x}=2^{10}\)
\(< =>1+2+3+...+x=10\)
\(=>6+x=10\)
\(=>x=10-6\)
\(=>x=4.\)
Nếu đúng thì k cho mình nhá
1) a, \(2.2^2.2^3....2^x=1024\)
\(\Rightarrow2^1.2^2.2^3...2^x=2^{10}\)
\(\Rightarrow2^{1+2+3+..+x}=2^{10}\)
\(\Rightarrow1+2+3+..+x=10\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=10\)
\(\Rightarrow x\left(x+1\right)=20\)
\(\Rightarrow x\left(x+1\right)=4.5\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
b, \(\frac{37-x}{x+13}=\frac{3}{7}\)
\(\Rightarrow\left(37-x\right).7=\left(x+13\right).3\)
\(\Rightarrow259-7x=3x+39\)
\(\Rightarrow259-39=7x+3x\)
\(\Rightarrow220=10x\)
\(\Rightarrow x=220:10\)
\(\Rightarrow x=22\)
Vậy \(x=22\)
2) \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+\left(\frac{50^2-15.125}{5^4}\right)^{2014}\)
\(=\frac{1}{2}.8-\frac{2}{5}+\left(\frac{5^4.2^2-5^4.3}{5^4}\right)^{2014}\)
\(=4-0,4+\left(\frac{5^4\left(2^2-3\right)}{5^4}\right)^{2014}\)
\(=3,6+\left(\frac{5^4.1}{5^4}\right)^{2014}\)
\(=3,6+1^{2014}\)
\(=3,6+1\)
\(=4,6\)
