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\(\dfrac{-2}{3}=\dfrac{18}{x}\\ \Rightarrow x=18:\dfrac{-2}{3}\\ \Rightarrow x=-27\)
a,x2.x3=25
=>x5=25
=>x=2
b,x+18=5.4^2
=>x=5.16-18
=>x=62
c,x.(x^2)^3=x^5
=>x.x5=x5
=>x=0,1
d,2x.7=224
2x=32
=>2x=25
=>x=5
e,(3x+5)2=289
=>(3x+5)2=172
=>3x+5=17
=>3x=12
=>x=4
g,32x+1.11=2673
=>32x=243
=>32x=35
=>x=\(\frac{5}{2}\)
\(3^2x+1=9x+1\)
\(9x+1=3^5.11\)
\(9x+1=2673\)
\(9x=2672\)
\(\Rightarrow x=296,888.......9\)
Từ đó suy ra sai đề
a/ 27.3x =243
3x =243:27
3x=9
3x =32
x=2
b/ 64.4x =45
43 .4x=45
4x=45:43
4x=42
x=2
c/(3x+52) =289
(3x+52)=172
3x+5=17
3x=17-5
3x=12
x=12:3=4
d/32x+1 .11=2673
32x+1 =2673:11
32x+1 =243
32x+1 =35
2x+1=5
2x=5-1
2x=4
x=4:2
x=2
ta gọi phần trong ngoặc là A thì ta có
A nhân x = A
x= A-A
x=1
Đặt C = \(\frac{1}{1.101}+\frac{1}{2.102}+...+\frac{1}{10.110}\)
=> 100C = \(\frac{100}{1.101}+\frac{100}{2.102}+...+\frac{100}{10.110}\)
=> 100C = \(1-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\)
=> 100C = \(\left(1+\frac{1}{2}+...+\frac{1}{10}\right)-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\)
=> C = \(\frac{1+\frac{1}{2}+...+\frac{1}{10}-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)}{100}\)
Lại có B = \(\frac{1}{1.11}+\frac{1}{2.12}+...+\frac{1}{100.110}\)
=> 10B = \(\frac{10}{1.11}+\frac{10}{2.12}+...+\frac{10}{100.110}\)
=> 10B = \(1-\frac{1}{11}+\frac{1}{2}-\frac{1}{12}+...+\frac{1}{100}-\frac{1}{110}\)
=> 10B = \(\left(1+\frac{1}{2}+...+\frac{1}{100}\right)-\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{110}\right)\)
=> 10B = \(1+\frac{1}{2}+...+\frac{1}{10}-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)\)
=> B = \(\frac{1+\frac{1}{2}+...+\frac{1}{10}-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)}{10}\)
Khi đó \(\left(\frac{1}{1.101}+\frac{1}{2.102}+...+\frac{1}{10.110}\right)x=\frac{1}{1.11}+\frac{1}{2.12}+...+\frac{1}{100.110}\)
<=> C.x = B
<=> \(\frac{1+\frac{1}{2}+...+\frac{1}{10}-\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{110}\right)}{100}x=\frac{1+\frac{1}{2}+...+\frac{1}{10}-\left(\frac{1}{101}+\frac{1}{102}+..+\frac{1}{110}\right)}{10}\)
=> \(x=10\)
Vậy x = 10
\(3^{2x+1}.11=2673\)
\(3^{2x+1}\) = 2673 : 11
\(3^{2x+1}\) = 243
\(3^{2x+1}\) = \(3^5\)
=> 2x +1 = 5
2x = 5 - 1
2x = 4
x = 4 : 2
x = 2
nha