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\(1+2+3+...+x=500500\)
\(\Rightarrow\frac{x.\left(x+1\right)}{2}=500500\)
\(\Rightarrow x.\left(x+1\right)=1001000\)
\(\Rightarrow1000.1001\)
..
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1/2x + 1/5 = 2/3x - 1/4
=> 1/2x - 2/3x = -1/4 - 1/5
=> -1/6x = -9/20
=> x = -9/20 : (-1/6)
=> x = 27/10
\(\frac{1}{2}x+\frac{1}{5}=\frac{2}{3}x-\frac{1}{4}\)
\(\frac{1}{2}x=\frac{2}{3}x-\frac{1}{4}-\frac{1}{5}\)
\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}\)
\(\frac{1}{2}x=-\frac{9}{20}+\frac{2x}{3}-\frac{2x}{3}\)
\(-\frac{x}{6}=-\frac{9}{20}\)
\(6\left(-\frac{x}{6}\right)=6\left(-\frac{9}{20}\right)\)
\(-x=-\frac{27}{10}\)
\(\Rightarrow x=-\frac{27}{10}\)
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\(a,\left(2^x-3\right)^3-59=5\)
\(\Leftrightarrow\left(2^x-3\right)^3=64=4^3\)
\(\Leftrightarrow2^x-3=4\)
\(\Leftrightarrow2^x=7\)
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x-2/4=5+x/3
<=>x-x/3=5+2/4
<=>2x/3=11/2
<=>2x=33/2<=>x=33/4
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a)x={0;1}
b)x=5
c)x=8\
d)x=2
e)x=45
f)ko có giá trị nào của x thỏa mãn
g)x=4
a) x^50 = x
x^50 = x^1
=> x=0
(câu a ko chắc đâu)
b) 125 = x^3
5^3 = x^3
=>x=5
c) 64 = x^2
8^2 = x^2 và (-8)^2 = x^2
=> x= cộng trừ 8
d) 90 = 10 * 3^x
3^x= 90:10
3^x = 9
3^x = 3^2 và 3^x = (-3)^2
=> x= cộng trừ 3
e) Tớ nghĩ đề câu này kì kì nên tự ý sửa chút nhé.
(x- 6)^2 =9
TH1:
(x-6)^2 = 3^2
x-6 = 3
x= 9
TH2:
(x-6)^2= (-3)^2
x-6 =-3
x= 3
Vậy x= 3; 9
f) 5^x + 1 = 125
5^x = 124
=> x thuộc rỗng
g) 5^2 * 5^ (x-3) -2 * 5^2= 5^2 *3
5x : 53 * 52 - 50 = 75
5x : 53 * 52 = 125
5x : 53 = 5
5x = 625
5^x = 5^4
=> x=4
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\(3^{x+1}+3^{x+2}+3^{x+3}-4.3^x=315\)
\(\Leftrightarrow3^x.3+3^x.3^2+3^x.3^3-4.3^x=315\)
\(\Leftrightarrow3^x.3+3^x.9+3^x.27-4.3^x=315\)
\(\Leftrightarrow3^x.\left(3+9+27-4\right)=315\)
\(\Leftrightarrow3^x.35=315\)\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)\(\Leftrightarrow x=2\)
Vậy \(x=2\)
Bài làm :
Ta có :
\(3^{x+1}+3^{x+2}+3^{x+3}-4.3^x=315\)
\(\Leftrightarrow3^x.3+3^x.3^2+3^x.3^3-4.3^x=315\)
\(\Leftrightarrow3^x.3+3^x.9+3^x.27-4.3^x=315\)
\(\Leftrightarrow3^x.\left(3+9+27-4\right)=315\)
\(\Leftrightarrow3^x.35=315\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Leftrightarrow x=2\)
Vậy x=2
\(\frac{1}{2}.x+\frac{3}{5}.\left(x-2\right)=3\)
\(\frac{1}{2}.x+\frac{3}{5}.x+\frac{6}{5}=3\)
\(\frac{1}{2}.x+\frac{3}{5}.x=3-\frac{6}{5}\)
\(\left(\frac{1}{2}+\frac{3}{5}\right).x=\frac{9}{5}\)
\(\frac{11}{10}.x=\frac{9}{5}\)
\(x=\frac{9}{5}:\frac{11}{10}\)
\(x=\frac{18}{11}\)
\(\frac{1}{2}.x+\frac{3}{5}.\left(x-2\right)=3\)
\(\frac{1}{2}.x+\frac{3}{5}.x-\frac{6}{5}=3\)
\(\frac{1}{2}.x+\frac{3}{5}.x=3+\frac{6}{5}\)
\(\left(\frac{1}{2}+\frac{3}{5}\right).x=\frac{21}{5}\)
\(\frac{11}{10}.x=\frac{21}{5}\)
\(x=\frac{21}{5}:\frac{11}{10}\)
\(x=\frac{42}{11}\)