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a) \(3^{x-2}=27\cdot9\)
\(3^{x-2}=3^3\cdot3^2=3^5\)
\(\Rightarrow\)\(x-2=5\Rightarrow x=7\)
b) \(2^{x+1}+2^{x+3}=80\)
\(\Rightarrow2^{x+1}\left(1+2^2\right)=80\)
\(\Rightarrow2^{x+1}\cdot5=80\)
\(\Rightarrow2^{x+1}=16=2^4\)
\(\Rightarrow x+1=4\Rightarrow x=3\)
c) \(2^{2x-3}=16\cdot8\)
\(2^{2x-3}=2^4\cdot2^3=2^7\)
\(\Rightarrow2x-3=7\)
\(\Rightarrow2x=4\Rightarrow x=2\)
d) \(2^{x-2}\cdot2^x=64\)
\(\Rightarrow2^{x-2+x}=64=2^6\)
\(\Rightarrow x-2+x=6\)
\(\Rightarrow2x-2=6\)
\(\Rightarrow2x=8\Rightarrow x=4\)
Giải:
a) \(3^{x-2}=27.9\)
\(\Leftrightarrow3^{x-2}=3^3.3^2\)
\(\Leftrightarrow3^{x-2}=3^5\)
Vì \(3=3\)
Nên \(x-2=5\)
\(\Leftrightarrow x=5+2\)
\(\Leftrightarrow x=7\)
Vậy x = 7.
b) \(2^{x+1}+2^{x+3}=80\)
\(\Leftrightarrow2^{x+1}\left(1+2^2\right)=80\)
\(\Leftrightarrow2^{x+1}.5=80\)
\(\Leftrightarrow2^{x+1}=\dfrac{80}{5}=16\)
\(\Leftrightarrow2^{x+1}=2^4\)
Vì \(2=2\)
Nên \(x+1=4\)
\(\Leftrightarrow x=4-1\)
\(\Leftrightarrow x=3\)
Vậy x = 3.
c) \(2^{2x-3}=16.8\)
\(\Leftrightarrow2^{2x-3}=2^4.2^3\)
\(\Leftrightarrow2^{2x-3}=2^7\)
Vì \(2=2\)
Nên \(2x-3=7\)
\(\Leftrightarrow2x=7+3=10\)
\(\Leftrightarrow x=\dfrac{10}{2}=5\)
Vậy x = 5.
d) \(2^{x-2}.2^x=64\)
\(2^{2x-2}=2^6\)
Vì \(2=2\)
Nên \(2x-2=6\)
\(\Leftrightarrow2x=6+2=8\)
\(\Leftrightarrow x=\dfrac{8}{2}=4\)
Vậy x = 4.
Chúc bạn học tốt!
a) 2 - ( \(5\frac{3}{8}\)x X - \(\frac{5}{24}\)) = \(\frac{5}{12}\)
\(5\frac{3}{8}\)x X - \(\frac{5}{24}\)= \(\frac{19}{12}\)
\(5\frac{3}{8}\)x X = \(\frac{43}{24}\)
X = \(\frac{1}{3}\)
b) \(1\frac{2}{9}\): ( \(3\frac{1}{3}\)x X + \(\frac{1}{6}\)) = \(\frac{22}{23}\)
\(3\frac{1}{3}\)x X + \(\frac{1}{6}\) = \(\frac{23}{18}\)
\(3\frac{1}{3}\)x X = \(\frac{10}{9}\)
X =\(\frac{1}{3}\)
C) \(\frac{4}{5}\)x X - \(\frac{1}{2}\)x X + \(\frac{3}{4}\)x X = \(\frac{7}{40}\)
( \(\frac{4}{5}-\frac{1}{2}+\frac{3}{4}\)) x X = \(\frac{7}{40}\)
\(\frac{21}{20}\) x X = \(\frac{7}{40}\)
X =\(\frac{1}{6}\)
a) Ta có:+) \(\frac{12}{16}=\frac{-x}{4}\) <=> 12.4 = 16.(-x)
<=> 48 = -16x
<=> x = 48 : (-16) = -3
+) \(\frac{12}{16}=\frac{21}{y}\) <=> 12y = 21.16
<=> 12y = 336
<=> y = 336 : 12 = 28
+) \(\frac{12}{16}=\frac{z}{-80}\) <=> 12. (-80) = 16z
<=> -960 = 16z
<=> z = -960 : 16 = -60
b) Ta có: \(\frac{x+3}{7+y}=\frac{3}{7}\) <=> (x + 3).7 = 3(7 + y)
<=> 7x + 21 = 21 + 3y
<=> 7x = 3y
<=> \(\frac{x}{3}=\frac{y}{7}\)
Áp dụng t/c của dãy tỉ số bằng nhau, ta có:
\(\frac{x}{3}=\frac{y}{7}=\frac{x+y}{3+7}=\frac{20}{10}=2\)
=> \(\hept{\begin{cases}\frac{x}{3}=2\\\frac{y}{7}=2\end{cases}}\) => \(\hept{\begin{cases}x=2.3=6\\y=2.7=14\end{cases}}\)
Vậy ...
a, \(2.x^x=10.3^{12}+8.27^4\)
\(2.x^x=10.3^{12}+8.3^{12}\)
\(2.x^x=3^{12}.\left(10+8\right)\)
\(2.x^x=3^{12}.18\)
\(2.x^x=3^{12}.2.3^3\)
\(2.x^x=3^{15}.2\)
\(x^x=3^{15}\)( Hình như sai đề )
b,\(3^{2x+2}=9^{x+3}\)
\(3^{2x+2}=3^{2x+3}\)
a: =>15-(x-2)=-13-27=-40
=>x-2=15+40=55
hay x=57
b: =>5-x=-114+12=-102
=>x=107
c: \(\Leftrightarrow\left|x\right|=-1-5=-6\)(vô lý)
d: \(\Leftrightarrow\left|x-3\right|=3\)
=>x-3=3 hoặc x-3=-3
=>x=6 hoặc x=0
a/
<=> x - 3 + 5x = 5x + 6
<=> x + 5x - 5x = 6 + 3
<=> x = 9
b/
<=> 12 - x + 2 = 8
<=> -x = 8 - 12 - 2
<=> -x = -6
<=> x = 6
c/
<=> (x - 2/3)^2 = (5/4)^2
<=> x - 2/3 = 5/4
<=> x = 23/12 (tự quy đồng)
d/
<=> (3/4 - x)^3 = (-2)^3
<=> 3/4 - x = -2
<=> -x = -2 - 3/4
<=> -x = -11/4 (tự qđồng)
\(8-12x+6x^2-x^3\)
\(=\left(2-x\right)^3\)
\(125x^3-75x^2+15x-1\)
\(=\left(5x-1\right)^3\)
\(x^2-xz-9y^2+3yz\)
\(=\left(x-3y\right)\left(x+3y\right)-z\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-z\right)\)
\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^3+2x^2-6x-27\)
\(=x^3+5x^2+9x-3x^2-15x-27\)
\(=x\left(x^2+5x+9\right)-3\left(x^2+5x+9\right)\)
\(=\left(x-3\right)\left(x^2+5x+9\right)\)
\(12x^3+4x^2-27x-9\)
\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)
\(=\left(3x+1\right)\left(4x^2-9\right)\)
\(=\left(3x+1\right)\left(2x-3\right)\left(2x+3\right)\)
\(4x^4+4x^3-x^2-x\)
\(=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=x\left(x+1\right)\left(4x^2-1\right)\)
\(=x\left(x+1\right)\left(2x-1\right)\left(2x+1\right)\)
a) (5x - 1) : 3 + 1 = 4
=> (5x - 1) : 3 = 3
=> (5x - 1) = 9
=> 5x - 1 = 9
=> 5x = 10
=> x = 2
b) 54 : (16 - x) - 1=5
=> 54:(16-x) = 6
=> 16-x = 9
=> x = 7
a) x = 190
b) x = 344
c) x = 4
d) x = 20