1 ) Tìm x biết
a) \(x^{10}\cdot\left(x^2\right)^{10}\cdot\left(x^3\right)^{10}\cdot...\cdot\left(x^{10}\right)^{10}\)
b)\(\frac{1}{2}\cdot2^x+4\cdot2^x=9\cdot2^5\)
c)\(3\cdot2^{x+2}=5\cdot2^3\)
tìm x biết
1)\(-\frac{2}{3}\cdot\left(x-\frac{1}{4}\right)=\frac{1}{3}\cdot\left(2x-1\right)\)
2)\(\frac{1}{5}\cdot2^x+\frac{1}{5}\cdot2^{x+1}=\frac{1}{5}\cdot2^7+\frac{1}{3}\cdot2^8\)
a)\(\left(2^2+3\right)\cdot\left(x-5\right)+14=5^2124:2^2\)
b) \(3^2\cdot\left(x+1\right)-3=2^3+7^2\cdot2:14\)
c) \(2^2\cdot3\cdot\left(x+5\right)-6=\left(2^3+2^2\right)\cdot2^2\)
d) \(\left(2^2+1\right)\cdot\left(x+14\right)=5^2\cdot4+\left(2^5+3^2+7^2\right):2\)
e) \(\left(2^2-1\right)\cdot\left(x-1\right)=2^2+\left(6^2+2^6\right):\left(5^2\cdot2\right)\)
g) \(\left(3^2-2\right)\cdot\left(x-12\right)+35=5^2+279:3^2\)
nhìn thì cảm thấy khó nhưng lại rất dễ đó
1. Tính:
a)\(81^3:3^5\)
b)\(16\cdot2^4\cdot\frac{1}{32}\cdot2^3\)
2. Tìm x:
a) \(\left(x-1\right)^5=32\)
b) \(\left(2^3:4\right)\cdot2^{\left(x+1\right)}=64\)
tìm x
1, \(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
2, \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
3, \(x-\left(\frac{11}{12}-x\right)=x-\frac{3}{4}\)
4, \(-29-4\cdot|3x+6|=-41\)
5, \(\frac{1}{5}\cdot2x+\frac{1}{3}\cdot2^{x+1}=\frac{1}{5}\cdot2^7+\frac{1}{3}\cdot2^8\)
MỌI NGƯỜI LÀM ĐƯỢC CÂU NÀO THÌ LÀM GIÚP EM Ạ
\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x=0+\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)
\(\Leftrightarrow\frac{11}{15}x=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2}{5}\div\frac{11}{15}\)
\(\Leftrightarrow x=\frac{6}{11}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\times\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{50}{100}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{100}\)
\(\Leftrightarrow x+1=100\)
\(\Leftrightarrow x=100-1\)
\(\Leftrightarrow x=99\)
\(x-\left(\frac{11}{12}+x\right)=x-\frac{3}{4}\)
\(\Leftrightarrow x-\frac{11}{12}-x=x-\frac{3}{4}\)
\(\Leftrightarrow-\frac{11}{12}=x-\frac{3}{4}\)
\(\Leftrightarrow x=\frac{-11}{12}+\frac{3}{4}\)
\(\Leftrightarrow x=\frac{-11}{12}+\frac{9}{12}\)
\(\Leftrightarrow x=\frac{-2}{12}=\frac{-1}{6}\)
Tính nhanh
C=\(\frac{4^7\cdot2^8}{3\cdot2^{15}\cdot16^2-5\cdot2^2\cdot\left(2^{10}\right)^2}\)
Bài 1: Tính
a. \(\left(1+\frac{1}{1\cdot3}\right)\cdot\left(1+\frac{1}{2\cdot4}\right)\cdot\left(1+\frac{1}{3\cdot5}\right)+\left(1+\frac{1}{4\cdot6}\right).....\left(1+\frac{1}{99\cdot101}\right)\)
b. \(\left[\sqrt{0,64}+\sqrt{0,0001}-\sqrt{\left(-0,5\right)^2}\right]\div\left[3\cdot\sqrt{\left(0,04\right)^2}-\sqrt{\left(-2\right)^4}\right]\)
c. \(\frac{5.4^{15}\cdot9^9-4.3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot6^{15}-7\cdot6^{10}\cdot2^{20}\cdot3^6}{9\cdot6^{19}\cdot2^9-4\cdot3^{17}\cdot2^{26}}+0,\left(6\right)\)
Bài 2: Tìm x, y, z biết :
a. \(\left(x-10\right)^{1+x}=\left(x-10\right)^{x+2009}\left(x\in Z\right)\)
b. \(\left|x-2007\right|+\left|x-2008\right|+\left|y-2009\right|+\left|x-2010\right|=3\left(x,y\in N\right)\)
c. \(25-y^2=8\left(x-2009\right)^2\left(x,y\in Z\right)\)
d. \(2008\left(x-4\right)^2+2009\left|x^2-16\right|+\left(y+1\right)^2\le0\)
e. \(2x=3y\) ; \(4z=5x\) và \(3y^2-z^2=-33\)
Bài 3: Chứng minh rằng
a. \(1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{4^2}-...-\frac{1}{2009^2}>\frac{1}{2009}\)
b. \(\left[75\cdot\left(4^{2008}+4^{2007}+4^{2006}+...+4+1\right)+25\right]⋮100\)
Bài 4:
a. Tìm giá trị nhỏ nhất của biểu thức : \(M=\left(x^2+2\right)+\left|x+y-2009\right|+2005\)
b. So sánh: \(31^{11}\) và \(\left(-17\right)^{14}\)
c. So sánh: \(\left(\frac{9}{11}-0,81\right)^{2012}\) và \(\frac{1}{10^{4024}}\)
Bài 1 :\(a,=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{100^2}{99.101}\)
\(=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4...101}\)
\(=100.\frac{2}{101}=\frac{200}{101}\)
tính bằng cách hợp lí
a) \(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)
b) \(1\cdot2\cdot3\cdot4\cdot...\cdot8\cdot9-1\cdot2\cdot3\cdot4\cdot...\cdot7\cdot8-1\cdot2\cdot3\cdot...\cdot7\cdot8^2\)
c) \(\frac{\left(3\cdot4\cdot2^{16}\right)^2}{11\cdot2^{13}\cdot4^{11}-16^9}\)
giúp em với ạ
c) \(\frac{\left(3\cdot4\cdot2^{16}\right)}{11\cdot2^{13}\cdot4^{11}-16^9}=\frac{\left(3\cdot2^2\cdot2^{16}\right)^2}{11\cdot2^{13}\cdot2^{22}-2^{36}}\)
\(=\frac{9\cdot2^4\cdot2^{32}}{11\cdot2^{35}-2^{26}}\)
\(=\frac{9\cdot2^4\cdot2^{32}2^{ }}{\left(11-2\right)\cdot2^{35}}\)
\(=\frac{9\cdot2^4\cdot2^{32}}{9\cdot2^{35}}\)
\(=\frac{9\cdot1\cdot2^{32}}{9\cdot2^{31}}=\frac{2^{32}}{2^{31}}=2\)
câu 1) \(A=\frac{x+2\cdot y-3\cdot z}{x-2\cdot y+3\cdot z}\) Tính A biết x : y : z = 5 : 4 : 3
Câu 2) cho a,b,c khác 0 và \(\frac{a\cdot b}{a+b}\)= \(\frac{b\cdot c}{b+c}\)= \(\frac{c\cdot a}{c+a}\)
Tính A = \(\frac{a\cdot b^2+b\cdot c^2+c\cdot a^2}{a^3+b^3+c^3}\)
câu 3 ) Tìm x để biểu thức A = \(\frac{2016\cdot\left|x-2\right|+2018}{\left|x-2\right|+1}\) đạt giá trị lớn nhất
câu 4) Cho A = \(2\cdot2^2+3\cdot2^3+4\cdot2^4+5\cdot2^5+.......+20.2^{20}\) so sánh A với \(^{2^{25}}\)
Các bạn giúp mình với mai mình đi thi rồi, các bạn nhớ viết rõ cách làm ra nhé cảm ơn đã giúp mình. Thank
\(^{2^{25}}\) là \(2^{25}\) mé các bạn, mình sợ mọi người nhầm
Câu 1 : Bài giải
Theo đề bài : \(x\text{ : }y\text{ : }z=5\text{ : }4\text{ : }3\text{ }\Rightarrow\text{ }\frac{x}{5}=\frac{y}{4}=\frac{z}{3}=\frac{x+y-z}{5+4-3}=\frac{x+y-z}{6}=\frac{x-y+z}{5-4+3}=\frac{x-y+z}{4}\)
( Áp dụng t/c dãy tỉ số bằng nhau )
\(\Rightarrow\text{ }x+y-z=x-y+z\)
\(\Rightarrow\text{ }y=x-y+z+z-x=2z+y\)
\(A=\frac{x+2\cdot y-3\cdot z}{x-2\cdot y+3\cdot z}=\frac{\left(x+y-z\right)+\left(y-2z\right)}{\left(x-y+z\right)+\left(2z-y\right)}=\frac{\left(x+y-z\right)+\left(2z+y-2z\right)}{\left(x-y+z\right)+\left(2z-2z-y\right)}=\frac{\left(x+y-z\right)+y}{\left(x-y+z\right)+\left(-y\right)}\)
Đến đây chịu ! Nhưng giải gần xong rồi !
A=\(\frac{15\cdot3^{11}+4.27^4}{9^7}\)
B=\(\frac{2^{19}\cdot2^{73}+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
C=\(\frac{5\cdot12^3\cdot4^{11}-16^8}{\left(3\cdot2^{17}\right)^2}\)
D=\(\frac{4^7\cdot2^8}{3\cdot2^{15}\cdot16^2-5\cdot2^2\cdot\left(2^{10}\right)^2}\)