Tìm x:
5x + 2x . ( 23 . 5 - 32 . 4 ) + 52 = 43
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a, 2 3 x + 5 2 x = 2 5 2 + 2 3 - 33
8x+25x = 33
33x = 33
x = 1
b, 260 : x + 4 = 5 2 3 + 5 - 3 3 2 + 2 2
260:(x+4) = 5.13–3.13
x+4 = 260:26
x+4 = 10
x = 6
c, 720 : [ 41 - 2 x - 5 ] = 2 3 . 5
41–(2x–5) = 720:40
2x–5 = 41–18
2x = 28
x = 14
d, 3 2 - 2 x - 12 + 35 = 5 2 + 279 : 3 2
7(x–12)+35 = 56
7(x–12) = 21
x–12 = 3
x = 15
a: 3x=81
nên x=27
b: \(5\cdot4^x=80\)
\(\Leftrightarrow4^x=16\)
hay x=2
c: \(2^x=4^5:4^3\)
\(\Leftrightarrow2^x=2^4\)
hay x=4
a) 5.22 + (x + 3) = 52
5.4 + (x + 3) = 25
20 + (x + 3) = 25
x + 3 = 25 – 20
x + 3 = 5
x = 5 – 3 = 2
b) 23 + (x – 32) = 53 - 43
8 + (x – 9) = 125 – 64
8 + (x – 9) = 61
x – 9 = 61 – 8
x – 9 = 53
x = 53 + 9 = 62
a) \(5.2^2+\left(x+3\right)=5^2\)
\(x+3=5^2-5.2^2\)
\(x+3=25-20\)
\(x+3=5\)
\(x=2\)
b) \(2^3+\left(x-3^2\right)=5^3-4^3\)
\(8+\left(x-9\right)=125-64\)
\(x-9=53\)
\(x=62\)
a) \(S=1+2+2^2+..+2^{2022}\)
\(2S=2+2^2+2^3+...+2^{2023}\)
\(2S-S=2+2^2+2^3+...+2^{2023}-1-2-2^2-...-2^{2022}\)
\(S=2^{2023}-1\)
b) \(S=3+3^2+3^3+...+3^{2022}\)
\(3S=3^2+3^3+...+3^{2023}\)
\(3S-S=3^2+3^3+....+3^{2023}-3-3^2-...-3^{2022}\)
\(2S=3^{2023}-3\)
\(\Rightarrow S=\dfrac{3^{2023}-3}{2}\)
c) \(S=4+4^2+4^3+...+4^{2022}\)
\(4S=4^2+4^3+...+4^{2023}\)
\(4S-S=4^2+4^3+...+4^{2023}-4-4^2-...-4^{2022}\)
\(3S=4^{2023}-4\)
\(S=\dfrac{4^{2023}-4}{3}\)
d) \(S=5+5^2+...+5^{2022}\)
\(5S=5^2+5^3+...+5^{2023}\)
\(5S-S=5^2+5^3+...+5^{2023}-5-5^2-...-5^{2022}\)
\(4S=5^{2023}-5\)
\(S=\dfrac{5^{2023}-5}{4}\)
\(1\)) \(5-\left(10-x\right)=7\)
\(10-x=5-7\)
\(10-x=-2\)
\(x=10-\left(-2\right)\)
\(x=12\)
\(2\)) \(-32-\left(x-5\right)=0\)
\(x-5=-32-0\)
\(x-5=-32\)
\(x=-32+5\)
\(x=-27\)
17x + 3. ( -16x – 37) = 2x + 43 - 4x
<=>17x-48x-111=-2x+43
<=>-29x=154
<=> \(x=-\frac{154}{29}\)
-3. (2x + 5) -16 < -4. (3 – 2x)
\(\Leftrightarrow-6x-31< -12+8x.\)
\(\Leftrightarrow-14x< 19\Rightarrow x< -\frac{19}{14}\)
\(5x+2x\cdot\left(2^3\cdot5-3^2\cdot4\right)+5^2=4^3\)
\(\Rightarrow5x+2x\cdot\left(8\cdot5-9\cdot4\right)+25=64\)
\(\Rightarrow5x+2x\cdot\left(40-36\right)=64-25\)
\(\Rightarrow5x+2x\cdot4=39\)
\(\Rightarrow5x+8x=39\)
\(\Rightarrow x\cdot\left(5+8\right)=39\)
\(\Rightarrow13x=39\)
\(\Rightarrow x=\dfrac{39}{13}\)
\(\Rightarrow x=3\)
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