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NY
2
TN
3 tháng 11 2016
a)\(\left(x^4\right)^2=\frac{x^{12}}{x^5}\)
\(\Leftrightarrow x^8=x^7\)\(\Leftrightarrow x^8-x^7=0\)
\(\Leftrightarrow x^7\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^7=0\\x-1=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
b)\(x^{10}=25\cdot x^8\)
\(\Leftrightarrow x^{10}-25\cdot x^8=0\)
\(\Leftrightarrow x^8\left(x^2-25\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^8=0\\x^2-5^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\\left(x-5\right)\left(x+5\right)=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm5\end{cases}}\)
TN
1
12 tháng 9 2016
a) \(\left(x^4\right)^2=\frac{x^{12}}{x^5}\)
\(\Rightarrow x^8=x^7\)
\(\Rightarrow x^8:x^7=1\)
\(\Rightarrow x=1\)
Vậy x = 1
b) \(x^{10}=25.x^8\)
\(\Rightarrow x^{10}:x^8=25\)
\(\Rightarrow x^2=25\)
\(\Rightarrow x=\pm5\)
Vậy \(x=\pm5\)
2 tháng 10 2020
a) ( x - 1/5 )2 = 0
<=> x - 1/5 = 0
<=> x = 1/5
b) ( x - 2 )2 = 1
<=> ( x - 2 )2 = ( ±1 )2
<=> x - 2 = 1 hoặc x - 2 = -1
<=> x = 3 hoặc x = 1
c) ( 2x - 1 )3 = -8
<=> ( 2x - 1 )3 = (-2)3
<=> 2x - 1 = -2
<=> 2x = -1
<=> x = -1/2
d) ( x4 )2 = x12/x5
<=> x8 = x7
<=> x8 - x7 = 0
<=> x7( x - 1 ) = 0
<=> x7 = 0 hoặc x - 1 = 0
<=> x = 0 hoặc x = 1
e) x10 = 25x8
<=> x10 - 25x8 = 0
<=> x8( x2 - 25 ) = 0
<=> x8 = 0 hoặc x2 - 25 = 0
<=> x = 0 hoặc x = ±5
f) ( 2x + 3 )2 = 9/121
<=> ( 2x + 3 )2 = ( ±3/11 )2
<=> 2x + 3 = 3/11 hoặc 2x + 3 = -3/11
<=> x = -15/11 hoặc x = -18/11
2 tháng 10 2020
a) \(\left(x-\frac{1}{5}\right)^2=0\Leftrightarrow x-\frac{1}{5}=0\Leftrightarrow x=\frac{1}{5}\)
b) \(\left(x-2\right)^2=1\)
\(\Leftrightarrow\left(x-2\right)^2-1=0\)
\(\Leftrightarrow\left(x-2-1\right)\left(x-2+1\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
c) \(\left(2x-1\right)^3=-8\)
\(\Leftrightarrow\left(2x-1\right)^3+8=0\)
\(\Leftrightarrow\left(2x-1+8\right)\left[\left(2x-1\right)^2-8\left(2x-1\right)+64\right]=0\)
\(\Leftrightarrow2x+7=0\)
\(\Leftrightarrow x=\frac{-7}{2}\)
d) ĐKXĐ : \(x\ne0\)
\(\left(x^4\right)^2=\frac{x^{12}}{x^5}\)
\(\Leftrightarrow x^8=x^7\)
\(\Leftrightarrow x^8-x^7=0\)
\(\Leftrightarrow x^7\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\left(ktm\right)\\x=1\left(tm\right)\end{cases}\Leftrightarrow x=1}\)
e) ĐKXĐ : x khác 0
\(x^{10}=25x^8\)
\(\Leftrightarrow x^2=25\Leftrightarrow x=5\)
f) \(\left(2x+3\right)^2=\frac{9}{121}\)
\(\Leftrightarrow\left(2x+3+\frac{3}{11}\right)\left(2x+3-\frac{3}{11}\right)=0\)
\(\Leftrightarrow\left(2x+\frac{36}{11}\right)\left(2x+\frac{30}{11}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{-18}{11}\\x=-\frac{15}{11}\end{cases}}\)
8 tháng 4 2022
a: (x-3)2=49
=>x-3=7 hoặc x-3=-7
=>x=10 hoặc x=-4
b: \(\left(x^4\right)^2=\dfrac{x^{12}}{x^5}\)
\(\Leftrightarrow x^8-x^7=0\)
\(\Leftrightarrow x^7\left(x-1\right)=0\)
=>x=0 hoặc x=1
c: \(\Leftrightarrow x^{10}-25x^8=0\)
\(\Leftrightarrow x^8\left(x^2-25\right)=0\)
\(\Leftrightarrow x^8\left(x-5\right)\left(x+5\right)=0\)
hay \(x\in\left\{0;5;-5\right\}\)
23 tháng 9 2016
\(\left(\frac{1}{2}\right)^5\times x=\left(\frac{1}{2}\right)^7\)
\(x=\left(\frac{1}{2}\right)^7\div\left(\frac{1}{2}\right)^5\)
\(x=\left(\frac{1}{2}\right)^{7-5}=\left(\frac{1}{2}\right)^2=\frac{1}{4}\) .
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{9}{21}\right)^2\)
\(\left(\frac{3}{7}\right)^2\times x=\left(\frac{3}{7}\right)^4\)
\(x=\left(\frac{3}{7}\right)^4\div\left(\frac{3}{7}\right)^2\)
\(x=\left(\frac{3}{7}\right)^{4-2}=\left(\frac{3}{7}\right)^2=\frac{9}{49}\)
\(2^x=2\Rightarrow x=1\)
\(3^x=3^4\Rightarrow x=4\)
\(7^x=7^7\Rightarrow x=7\)
\(\left(-3\right)^x=\left(-3\right)^5\Rightarrow x=5\)
\(\left(-5\right)^x=\left(-5\right)^4\Rightarrow x=4\)
\(2^x=4\Leftrightarrow2^x=2^2\Rightarrow x=2\)
\(2^x=8\Leftrightarrow2^x=2^3\Rightarrow x=3\)
\(2^x=16\Leftrightarrow2^x=2^4\Rightarrow x=4\)
\(3^{x+1}=3^2\Leftrightarrow x+1=2\Leftrightarrow x=2-1\Rightarrow x=1\)
\(5^{x-1}=5\Leftrightarrow x-1=1\Leftrightarrow x=1+1\Rightarrow x=2\)
\(6^{x+4}=6^{10}\Leftrightarrow x+4=10\Leftrightarrow x=10-4\Rightarrow x=6\)
\(5^{2x-7}=5^{11}\Leftrightarrow2x-7=11\Leftrightarrow2x=11+7\Leftrightarrow2x=18\Leftrightarrow x=18\div2\Rightarrow x=9\)
\(\left(-2\right)^{4x+2}=64\)
\(2^{-4x+2}=2^6\Leftrightarrow-4x+2=6\Leftrightarrow-4x=6-2\Leftrightarrow-4x=4\Leftrightarrow x=4\div\left(-4\right)\Rightarrow x=-1\)
\(\left(\frac{1}{2}\right)^x=\left(\frac{1}{2}\right)^5\Rightarrow x=5\)
\(\left(\frac{5}{6}\right)^{2x}=\left(\frac{5}{6}\right)^5\Rightarrow2x=5\Rightarrow x=\frac{5}{2}\)
\(\left(\frac{3}{4}\right)^{2x-1}=\left(\frac{3}{4}\right)^{5x-4}\Rightarrow2x-1=5x-4\)
\(2x-5x=-4+1\)
\(-3x=-3\Rightarrow x=1\)
\(\left(\frac{-1}{10}\right)^x=\frac{1}{100}\)
\(\left(\frac{1}{10}\right)^{-x}=\left(\frac{1}{10}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{2}\right)^x=\frac{9}{4}\)
\(\left(\frac{3}{2}\right)^{-x}=\left(\frac{3}{2}\right)^2\Rightarrow-x=2\Rightarrow x=-2\)
\(\left(\frac{-3}{5}\right)^{2x}=\frac{9}{25}\)
\(\left(\frac{3}{5}\right)^{-2x}=\left(\frac{3}{5}\right)^2\Rightarrow-2x=2\Rightarrow x=-1\)
\(\left(\frac{-2}{3}\right)^x=\frac{-8}{27}\)
\(\left(\frac{-2}{3}\right)^x=\left(\frac{-2}{3}\right)^3\Rightarrow x=3\).
hehe.
đánh tới què tay, hoa mắt lun r nekkk!!
26 tháng 2 2022
c: \(=\dfrac{7}{23}\cdot\dfrac{-24-45}{18}=\dfrac{7}{23}\cdot\dfrac{-69}{18}=\dfrac{7}{18}\cdot\left(-3\right)=-\dfrac{7}{6}\)
d: \(=\dfrac{7}{5}\left(23+\dfrac{1}{4}-13-\dfrac{1}{4}\right)=\dfrac{7}{5}\cdot10=14\)
e: \(=\dfrac{2^5\cdot3^3\cdot5^3}{2^3\cdot3^3\cdot2^2\cdot5^2}=5\)
i: \(=\dfrac{1}{3^{10}}\cdot3^{50}-\dfrac{2^{10}}{3^{10}}:\dfrac{4^5}{9^5}=3^{40}-1\)