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Bài 1:
a)
\(\dfrac{4^2\cdot25^2+32\cdot125}{2^3\cdot5^2}\\ =\dfrac{\left(2^2\right)^2\cdot\left(5^2\right)^2+2^5\cdot5^3}{2^3\cdot5^2}\\ =\dfrac{2^{2\cdot2}\cdot5^{2\cdot2}+2^5\cdot5^3}{2^3\cdot5^2}\\ =\dfrac{2^4\cdot5^4+2^5\cdot5^3}{2^3\cdot5^2}\\ =\dfrac{2^4\cdot5^4}{2^3\cdot5^2}+\dfrac{2^5\cdot5^3}{2^3\cdot5^2}\\ =2\cdot5^2+2^2\cdot5\\ =2\cdot25+4\cdot5\\ =50+20\\ =70\)
c)
\(\dfrac{\left(1-\dfrac{4}{9}-2\right)\cdot16}{\left(2-3\right)^{-2}}+12\\ =\dfrac{\left(\dfrac{9}{9}-\dfrac{4}{9}-\dfrac{18}{9}\right)\cdot16}{\left(-1\right)^{-2}}+12\\ =\dfrac{\dfrac{-13}{9}\cdot16}{\dfrac{1}{\left(-1\right)^2}}+12\\ =\dfrac{\dfrac{-208}{9}}{1}+12\\ =\dfrac{-208}{9}+12\\ =\dfrac{-208}{9}+\dfrac{108}{9}\\ =\dfrac{100}{9}\)
Bài 2:
a)
\(\left(x+2\right)^2=36\\ \Rightarrow\left[{}\begin{matrix}x+2=6\\x+2=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)
b)
\(\left(1,78^{2x-2}-1,78^x\right):1,78^x=0\\ \Leftrightarrow\dfrac{1,78^{2x-2}}{1,78^x}-\dfrac{1,78^x}{1,78^x}=0\\ \Leftrightarrow\dfrac{1,78^{2x-2}}{1,78^x}-1=0\\ \Leftrightarrow \dfrac{1,78^{2x-2}}{1,78^x}=1\\ \Leftrightarrow1,78^{2x-2}=1,78^x\\ \Leftrightarrow2x-2=x\\ \Leftrightarrow2x-x=2\\ \Leftrightarrow x=2\)
d) \(5^{\left(x-2\right)\left(x+3\right)}=1\)
\(\Rightarrow5^{\left(x-2\right)\left(x+3\right)}=5^0\)
\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
Vậy \(x_1=-3;x_2=2\)
1) Tìm số nguyên x, biết :
a) 3x = 94/ 273
3x = 1/3
3x = 3-1
=> x = -1
b) 3x = 98 / 273 . 812
3x = 37.38
3x = 315
=> x = 15
c) 2x - 3 / 410 = 83
2x - 3 = 83.410
2x - 3 = 226
=> x - 3 = 26
=> x = 29
d) 22x - 3 / 410 = 83 . 165
22x - 3 / 410 = 269
22x - 3 = 269 . 410
22x - 3 = 289
=> 2x - 3 = 89
2x = 91
x = 91/2
e) 35 / 3x = 310
3x = 35 : 310
3x = 3-5
=> x = -5
a/ \(\Leftrightarrow3^{2x}:3^2=\left(\frac{1}{3}\right)^5\Rightarrow3^x=\frac{1}{3^5}\Rightarrow3^x.3^5=1\Rightarrow3^{5x}=3^0\)
=> 5x = 0 => x = 0
a. x2 + 1 = 82
=> x2 = 81
=> x2 = 92
=> x = 9 hoặc x = - 9
b. x2 + 7/4 = 23/4
=> x2 = 4
=> x2 = 22
=> x = 2 hoặc x = - 2
c. ( 2x + 3 )2 = 25
=> ( 2x + 3 )2 = 52
=> 2x + 3 = 5 hoặc 2x + 3 = - 5
=> x = 1 hoặc x = - 4
a, \(x^2+1=82\Leftrightarrow x^2=81\Leftrightarrow x=\pm9\)
b, \(x^2+\frac{7}{4}=\frac{23}{4}\Leftrightarrow x^2=4\Leftrightarrow x=\pm2\)
c, \(\left(2x+3\right)^2=25\Leftrightarrow2x+3=\pm5\Leftrightarrow\orbr{\begin{cases}2x+3=5\\2x+3=-5\end{cases}\Leftrightarrow\orbr{\begin{cases}x=4\\x=-1\end{cases}}}\)
\(3^{2x+1}=243\)
\(\Leftrightarrow3^{2x+1}=3^5\)
\(\Leftrightarrow2x+1=5\)
\(\Leftrightarrow2x=4\)
\(\Leftrightarrow x=2\)
1) 32x + 1 = 243
32x + 1 = 35
2x + 1 = 5
2x = 5 - 1
2x = 4
x = 2
3) 96 - 3(x + 1) = 42
-3(x + 1) = 42 - 96
-3(x + 1) = -54
x + 1 = (-54) : (-3)
x + 1 = 18
x = 18 - 1
x = 17
3) 100 - 3(x - 2) = 91
-3(x - 2) = 91 - 100
-3(x - 2) = -9
x - 2 = (-9) : (-3)
x - 2 = 3
x = 3 + 2
x = 5