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a: x/5=32/80
nên x/5=2/5
hay x=2
13/x=26/30
nên 13/x=13/15
hay x=15
-x/7=22/-77
=>x/7=2/7
hay x=2
b: x/9=28/36
=>x/9=7/9
hay x=7
-10/x=50/55
=>-10/x=10/11
hay x=-11
\(f\)) \(32^{-x}.16^x=1024\)
\(\left(2\right)^{-5x}.2^{4x}=2^{10}\)
\(\Leftrightarrow2^{4x-5x}=2^{10}\)
\(\Leftrightarrow2^{-x}=2^{10}\)
\(\Leftrightarrow-x=10\)
\(\Leftrightarrow x=-10\)
\(g\)) \(3^{x-1}.5+3^{x-1}=162\)
\(3^{x-1}.\left(5+1\right)=162\)
\(3^{x-1}.6=162\)
\(3^{x-1}=162:6\)
\(3^{x-1}=27\)
\(\Leftrightarrow3^{x-1}=3^3\)
\(\Leftrightarrow x-1=3\)
\(\Leftrightarrow x=4\)
\(h\)) \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^8=0\)
\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^6.\left(2x-1\right)^2=0\)
\(\Leftrightarrow\left(2x-1\right)^6.\left[1-\left(2x-1\right)^2\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(2x-1\right)^6=0\\1-\left(2x-1\right)^2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x-1=0\\\left(2x-1\right)^2=1\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}2x=1\\\left(2x-1\right)^2=\left(1,-1\right)^2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\2x-1=-1\\2x-1=1\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\2x=0\\2x=2\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\x=0\\x=1\end{cases}}\)
\(i\)) \(5^x+5^{x+2}=650\)
\(5^x.\left(1+5^2\right)=650\)
\(5^x.26=650\)
\(5^x=650:26\)
\(5^x=25\)
\(\Leftrightarrow5^x=5^2\)
\(\Leftrightarrow x=2\)
Bài 1:
\(\text{a) }x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
\(=x^{1+2+3+4+5+...+49+50}\)
\(=x^{\frac{51.50}{2}}\)
\(=x^{1275}\)
\(\text{b) Ta có:}\)
\(4^{15}=\left(2^2\right)^{15}=2^{2.15}=2^{30}\)
\(8^{11}=\left(2^3\right)^{11}=2^{3.11}=2^{33}\)
\(\text{Vì }2^{30}< 2^{33}\text{ nên }4^{15}< 8^{11}\)
Bài 2: Tìm x
\(\left(x-1\right)^4:3^2=3^6\)
\(\Rightarrow\left(x-1\right)^4=3^6\times3^2\)
\(\Rightarrow\left(x-1\right)^4=3^8\)
\(\Rightarrow\left(x-1\right)^4=3^{2.4}\)
\(\Rightarrow\left(x-1\right)^4=\left(3^2\right)^4\)
\(\Rightarrow x-1=9\)
\(\Rightarrow x=10\)
Bài 3 và bài 4 mk làm sau
Bài 1 : a) \(x.x^2.x^3.x^4.....x^{49}.x^{50}=x^{1+2+3+...+49+50}\) (Dễ rồi tự tính)
b) \(\hept{\begin{cases}4^{15}=\left(2^2\right)^{15}=2^{30}\\8^{11}=\left(2^3\right)^{11}=2^{33}\end{cases}}\)Rồi tự so sánh đi
Bài 2 :
\(\left(x-1\right)^4\div3^2=3^6\Leftrightarrow\left(x-1\right)^4=3^8=\left(3^2\right)^4=9^4\Leftrightarrow x-1=9\Leftrightarrow x=10\)
Bài 3 :
\(\hept{\begin{cases}27^{15}=\left(3^3\right)^{15}=3^{45}\\81^{11}=\left(3^4\right)^{11}=3^{44}\end{cases}}\) nt
1.
a) \(x\in\left\{0;32;64;96\right\}\)
b) \(x\in\left\{41;82;123;164\right\}\)
c) \(x\in\left\{1;2;5;10;25;50\right\}\)
2.
a) \(x\in\left\{0;2;3;4;7\right\}\)
b) \(x=2\)
#)Giải :
a) 36 chia hết cho \(x-1\)
\(\Rightarrow x-1\inƯ\left(36\right)=\left\{1;2;3;6;9;12;18;36\right\}\)
\(\Rightarrow x\in\left\{2;3;4;7;10;13;19;36\right\}\)
b) \(x-1\)là ước của 32
\(\Rightarrow x-1\in\left\{1;2;4;8;16;32\right\}\)
\(\Rightarrow x\in\left\{2;3;5;9;17;33\right\}\)
c) 45 là bộ của \(x-2\)
\(\Rightarrow x-2\inƯ\left(45\right)=\left\{1;3;5;9;15;45\right\}\)
\(\Rightarrow x\in\left\{3;5;7;11;17;47\right\}\)
b./ \(\Leftrightarrow\frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+10}{2000}+1+\frac{x+11}{1999}+1+\frac{x+12}{1998}+1.\)
\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}\right)=0\)(b)
Mà \(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}< 0\)
(b) \(\Leftrightarrow x+2010=0\Leftrightarrow x=-2010\)
a./
\(\Leftrightarrow\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}-\frac{x+1}{5}-\frac{x+1}{6}=0.\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)(a)
Mà \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}>0\)
(a) \(\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
\(\left(2\frac{4}{5}x-50\right)\div\frac{2}{3}=51\)
\(\frac{14}{5}x-50=51\times\frac{2}{3}\)
\(\frac{14}{5}x-50=34\)
\(\frac{14}{5}x=84\)
\(x=84\times\frac{5}{14}\)
\(x=30\)
\(a,\left(2\frac{4}{5}.x-50\right):\frac{2}{3}=51\)
\(\left(\frac{14}{5}.x-50\right):\frac{2}{3}=51\)
\(\frac{14}{5}.x-50=51\times\frac{2}{3}\)
\(\frac{14}{5}.x-50=34\)
\(\frac{14}{5}.x=34+50\)
\(\frac{14}{5}.x=84\)
\(x=84:\frac{14}{5}\)
\(x=\frac{405}{14}\)
a, \(2\cdot2^2\cdot2^3\cdot2^4\cdot...\cdot2^x=1024\)
\(\Leftrightarrow2^{1+2+3+4+...+x}=2^{10}\Leftrightarrow1+2+3+4+...+x=10\)
\(\Rightarrow\left(x+1\right)x\div2=10\Rightarrow\left(x+1\right)x=20\)
Vì : ( x + 1 ) x là hai số tự nhiên liên tiếp \(\Rightarrow x=4\in Z\)
Vậy x = 4
b, \(9.27< 3^x< 243\Leftrightarrow3^5< 3^x< 3^5\)
\(\Rightarrow5< x< 5\Rightarrow x\in\varnothing\)
Vậy \(x\in\varnothing\)
a ) (2,8x - 32 ) : 2/3 = -90
<=> 2,8x -32 = -60
<=> 2,8x = -28
<=> x = -10
b ) 4/5 + 5/7 :x =1/6
<=> 5/7:x = -19/30
<=> x = -150/133
a)\(\left(2,8x-32\right):\frac{2}{3}=-90\)
\(2,8x-32=-90\cdot\frac{2}{3}\)
\(2,8x-32=-60\)
\(2,8x=-60+32\)
\(2,8x=-28\)
\(x=-28:2,8\)
\(x=-10\)
Vậy x = -10
b) \(\frac{4}{5}+\frac{5}{7}:x=\frac{1}{6}\)
\(\frac{5}{7}:x=\frac{1}{6}-\frac{4}{5}\)
\(\frac{5}{7}:x=\frac{-19}{30}\)
\(x=\frac{5}{7}:\frac{-19}{30}\)
\(x=\frac{-150}{133}\)
Vậy x = -150/133
=))
@Nguyễn Ngọc Linh Châu
\(2^x.32=1024\)
\(\Rightarrow2^x.2^5=2^{10}\)
\(\Rightarrow2^x=2^5\Leftrightarrow x=5\)
\(x^{50}=x\Leftrightarrow x^{50}-x=0\Leftrightarrow x\left(x^{49}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^{49}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
a,\(2^x.32=1024\)
\(\Leftrightarrow2^x.2^5=2^{10}\)
\(\Rightarrow2^x=2^{10}:2^5=2^5\)
\(\Rightarrow2^x=2^5\)
b,\(x^{50}=x\)
\(\Leftrightarrow1^{50}=1\)
\(\Rightarrow x=1\)