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\(9^x:3^x=3^7\)
\(\Rightarrow9:3^x=3^7\)
\(\Rightarrow3^x=3^7\)
\(\Rightarrow x=7\)
\(\left(\frac{4}{9}\right)^n=\left(\frac{2}{3}\right)^5\)
<=>\(\left(\frac{2}{3}\right)^{\frac{n}{2}}=\left(\frac{2}{3}\right)^5\)
<=>\(\frac{n}{2}=5\)
<=>n=10
\(\left(\frac{4}{9}\right)^n=\left(\frac{2}{3}\right)^5\)
\(\Rightarrow\left(\frac{2}{3}\right)^{2n}=\left(\frac{2}{3}\right)^5\)
\(\Rightarrow2n=5\Rightarrow n=\frac{5}{2}\)
Vậy n = 5/2
a.\(3^{-2}.3^2.27^x=\frac{1}{3}\)
\(\Rightarrow3^{-2+2}.\left(3^3\right)^x=\frac{1}{3}\)
\(\Rightarrow3^0.3^{3x}=3^{-1}\)
\(\Rightarrow3^{3x}=3^{-1}\)
=> 3x=-1
=> x=\(-\frac{1}{3}\)
b.\(7^{x+2}+2.7^{x-1}=345\)
\(\Rightarrow7^{x-1}.\left(7^3+2\right)=345\)
\(\Rightarrow7^{x-1}.345=345\)
=> 7x-1=345 : 345
=> 7x-1=1
=> 7x-1=70
=> x-1=0
Vậy x=1.
c.\(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Rightarrow\left(2x-1\right)\in\left\{-1;0;1\right\}\)
=> 2x-1=-1 hoặc 2x-1=0 hoặc 2x-1=1
=> 2x=0 hoặc 2x=1 hoặc 2x=2
=> x=0 hoặc x=\(\frac{1}{2}\) hoặc x=1
Vậy \(x\in\left\{0;\frac{1}{2};1\right\}\)
b) -7/9 - (1/3 - x)^2 : 2 = -1
-(1/3 - x)^2 : 2 = -1 + 7/9
-(1/3 - x)^2 : 2 = -2/9
-(1/3 - x)^2 = -2/9.2
-(1/3 - x)^2 = -4/9
(1/3 - x)^2 = 4/9
(1/3 - x)^2 = (-+2/3)^2
1/3 - x = -+2/3
1/3 - x = -2/3 hoặc 1/3 - x = 2/3
x = -2/3 + 1/3 x = 2/3 + 1/3
x = -1/3 x = 1
Làm câu sau nha ! Câu đầu Chihiro làm đúng rồi nha ! Có thể sai sót đôi chỗ ! Bạn tính lại bằng máy tính nha !
\(\left[2^2+\left(2^2\right)^3\right]\cdot x+3^4\cdot x=2^2\cdot3^7+1\)
\(\left[4+64\right]\cdot x+81\cdot x=4\cdot2187+1\)
\(68\cdot x+81\cdot x=8748+1\)
\(x\left(68+81\right)=8749\)
\(x\cdot139=8749\)
\(x=8749\text{ : }139\)
\(x=\frac{8749}{139}\)
1a) \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)
=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\\frac{3}{2}x+\frac{1}{2}=1-4x\end{cases}}\)
=> \(\orbr{\begin{cases}-\frac{5}{2}x=-\frac{3}{2}\\\frac{11}{2}x=\frac{1}{2}\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{1}{11}\end{cases}}\)
b) \(\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)
=>\(\left|\frac{5}{4}x-\frac{7}{2}\right|=\left|\frac{5}{8}x+\frac{3}{5}\right|\)
=> \(\orbr{\begin{cases}\frac{5}{4}x-\frac{7}{2}=\frac{5}{8}x+\frac{3}{5}\\\frac{5}{4}x-\frac{7}{2}=-\frac{5}{8}x-\frac{3}{5}\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{5}{8}x=\frac{41}{10}\\\frac{15}{8}x=\frac{29}{10}\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)
c) TT
a, \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)
=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\-\frac{3}{2}x-\frac{1}{2}=4x-1\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}-4x=-1\\-\frac{3}{2}x-\frac{1}{2}-4x=-1\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{3}{5}\\x=\frac{1}{11}\end{cases}}\)
\(b,\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)
=> \(\left|\frac{5}{4}x-\frac{7}{2}\right|-0=\left|\frac{5}{8}x+\frac{3}{5}\right|\)
=> \(\frac{\left|5x-14\right|}{4}=\frac{\left|25x+24\right|}{40}\)
=> \(\frac{10(\left|5x-14\right|)}{40}=\frac{\left|25x+24\right|}{40}\)
=> \(\left|50x-140\right|=\left|25x+24\right|\)
=> \(\orbr{\begin{cases}50x-140=25x+24\\-50x+140=25x+24\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)
c, \(\left|\frac{7}{5}x+\frac{2}{3}\right|=\left|\frac{4}{3}x-\frac{1}{4}\right|\)
=> \(\orbr{\begin{cases}\frac{7}{5}x+\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\\-\frac{7}{5}x-\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{55}{4}\\x=-\frac{25}{164}\end{cases}}\)
Bài 2 : a. |2x - 5| = x + 1
TH1 : 2x - 5 = x + 1
=> 2x - 5 - x = 1
=> 2x - x - 5 = 1
=> 2x - x = 6
=> x = 6
TH2 : -2x + 5 = x + 1
=> -2x + 5 - x = 1
=> -2x - x + 5 = 1
=> -3x = -4
=> x = 4/3
Ba bài còn lại tương tự
\(\left(\frac{1}{2}\right)^5\times x=\left(\frac{1}{2}\right)^7\)
\(x=\left(\frac{1}{2}\right)^7\div\left(\frac{1}{2}\right)^5\)
\(x=\left(\frac{1}{2}\right)^{7-5}=\left(\frac{1}{2}\right)^2=\frac{1}{4}\) .
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{9}{21}\right)^2\)
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{3}{7}\right)^4\)
\(x=\left(\frac{3}{7}\right)^4\div\left(\frac{3}{7}\right)^2\)
\(x=\left(\frac{3}{7}\right)^{4-2}=\left(\frac{3}{7}\right)^2=\frac{9}{49}\)
\(2^x=2\Rightarrow x=1\)
\(3^x=3^4\Rightarrow x=4\)
\(7^x=7^7\Rightarrow x=7\)
\(\left(-3\right)^x=\left(-3\right)^5\Rightarrow x=5\)
\(\left(-5\right)^x=\left(-5\right)^4\Rightarrow x=4\)
\(2^x=4\Leftrightarrow2^x=2^2\Rightarrow x=2\)
\(2^x=8\Leftrightarrow2^x=2^3\Rightarrow x=3\)
\(2^x=16\Leftrightarrow2^x=2^4\Rightarrow x=4\)
\(3^{x+1}=3^2\Leftrightarrow x+1=2\Leftrightarrow x=2-1\Rightarrow x=1\)
\(5^{x-1}=5\Leftrightarrow x-1=1\Leftrightarrow x=1+1\Rightarrow x=2\)
\(6^{x+4}=6^{10}\Leftrightarrow x+4=10\Leftrightarrow x=10-4\Rightarrow x=6\)
\(5^{2x-7}=5^{11}\Leftrightarrow2x-7=11\Leftrightarrow2x=11+7\Leftrightarrow2x=18\Leftrightarrow x=18\div2\Rightarrow x=9\)
\(\left(-2\right)^{4x+2}=64\)
\(2^{-4x+2}=2^6\Leftrightarrow-4x+2=6\Leftrightarrow-4x=6-2\Leftrightarrow-4x=4\Leftrightarrow x=4\div\left(-4\right)\Rightarrow x=-1\)
\(\left(\frac{1}{2}\right)^x=\left(\frac{1}{2}\right)^5\Rightarrow x=5\)
\(\left(\frac{5}{6}\right)^{2x}=\left(\frac{5}{6}\right)^5\Rightarrow2x=5\Rightarrow x=\frac{5}{2}\)
\(\left(\frac{3}{4}\right)^{2x-1}=\left(\frac{3}{4}\right)^{5x-4}\Rightarrow2x-1=5x-4\)
\(2x-5x=-4+1\)
\(-3x=-3\Rightarrow x=1\)
\(\left(\frac{-1}{10}\right)^x=\frac{1}{100}\)
\(\left(\frac{1}{10}\right)^{-x}=\left(\frac{1}{10}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{2}\right)^x=\frac{9}{4}\)
\(\left(\frac{3}{2}\right)^{-x}=\left(\frac{3}{2}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{5}\right)^{2x}=\frac{9}{25}\)
\(\left(\frac{3}{5}\right)^{-2x}=\left(\frac{3}{5}\right)^2\Rightarrow-2x=2\Rightarrow x=-1\)
\(\left(\frac{-2}{3}\right)^x=\frac{-8}{27}\)
\(\left(\frac{-2}{3}\right)^x=\left(\frac{-2}{3}\right)^3\Rightarrow x=3\).
hehe.
đánh tới què tay, hoa mắt lun r nekkk!!
Bài 1:
\(4.\left(\frac{-1}{2}\right)^2-2.\left(\frac{-1}{2}\right)^2+3.\left(\frac{-1}{2}\right)+1\)
\(=4.\frac{1}{4}-2.\frac{1}{4}+3.\left(\frac{-1}{2}\right)+1\)
\(=1-\frac{1}{2}-\frac{3}{2}+1\)
\(=0\)
Bài 2:
a) \(\frac{37-x}{x+13}=\frac{3}{7}\)
\(\Rightarrow7\left(37-x\right)=3\left(x+13\right)\)
\(\Rightarrow259-7x=3x+39\)
\(\Rightarrow259-39=3x+7x\)
\(\Rightarrow220=10x\)
\(\Rightarrow x=22\)
d) \(\frac{3^2.3^8}{27^3}=3^x\)
\(\Rightarrow\frac{3^{10}}{\left(3^3\right)^3}=3^x\)
\(\frac{\Rightarrow3^{10}}{3^9}=3^x\)
\(\Rightarrow3=3^x\)
\(\Rightarrow x=1\)
Hok tốt nha^^
a) 7x+2 + 2.7x-1 = 345
7x-1 . 73 + 2.7x-1 = 345
7x-1.(343+2) = 345
7x-1. 345=345
=> 7x-1=1
=> 7x-1=70
=> x-1 =0
x=1
b)\(\frac{1}{2}\).2x + 2x+2= 28+25
\(\frac{1}{2}\).2x + 2x . 22 = 288
2x . ( \(\frac{1}{2}\)+ 4)= 288
2x . \(\frac{9}{2}\)=288
=>2x=64
2x= 26
=>x=6
c)2.3x +3x-1 = 7.( 32+2.62)
2.3x-1.31 + 3x-1 = 567
3x-1.(6+1)=567
3x-1.7=567
=>3x-1= 81
3x-1=34
=>x-1=4
x=5