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a: Ta có: \(60-3\left(x-2\right)=51\)
\(\Leftrightarrow3\left(x-2\right)=9\)
\(\Leftrightarrow x-2=3\)
hay x=5
b: Ta có: \(4x-20=2^5:2^3\)
\(\Leftrightarrow4x=24\)
hay x=6
a) x=3
b) x=1
c) x=1 hoặc -5
d) x=2
e) x=2
g) x=2
h) x=1 hoặc x=0 hoặc x=-1
i) x=-1 hoặc x=0
\(a.4^x=64\)
\(4^x=4^3\)
\(\Rightarrow x=3\)
\(b,3^{x\times4}=81\)
\(3^{x\times4}=3^4\)
\(x\times4=4\)
\(\Rightarrow x=1\)
\(c,\left(2+x\right)^4=81\)
\(\left(2+x\right)^4=3^4\)
\(2+x=3\)
\(x=3-2\)
\(x=1\)
\(d,5^{x\times5}=125\)
\(5^{x\times5}=5^3\)
\(x\times5=3\)
\(x=3:5\)
\(x=\frac{3}{5}\)
Bài 1 :
\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)
\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)
\(\Rightarrow M< N\)
Bài 3 :
a) \(t^2+5t-8\) khi \(t=2\)
\(=5^2+2.5-8\)
\(=25+10-8\)
\(=27\)
b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)
\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)
\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)
c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)
\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)
\(\left(1\right)=1^3=1\)
a) 27 . 3x = 310
27 . 3x = 59049
3x = 59049 : 27
3x = 2187
3x = 37
x = 7
b) 60 + 3x = 910 : 98
60 + 3x = 92
60 + 3x = 81
3x = 81 - 60
3x = 21
x = 21 : 3
x = 7
c) 23 - 3(4+x ) = 3
3( 4 + x ) = 23 - 3
3( 4 + x ) = 20
Đề bài sai nha bạn
a) \(27.3^x=3^{10}\)
\(3^3.3^x=3^{10}\)
\(3^{3+x}=3^{10}\)
\(\Rightarrow3+x=10\)
\(\Rightarrow x=7\)
vậy \(x=7\)
b) \(60+3x=9^{10}:9^8\)
\(60+3x=9^{10-8}\)
\(60+3x=9^2\)
\(60+3x=81\)
\(3x=81-60\)
\(3x=21\)
\(x=7\)
vậy \(x=7\)
c) \(23-3\left(4+x\right)=3\)
\(23-12-3x=3\)
\(11-3x=3\)
\(3x=11-3\)
\(3x=8\)
\(x=\frac{8}{3}\)
vậy \(x=\frac{8}{3}\)
a,S=1+3+32+...+360
3S=3+32+33+...+361
3S-S=(3+32+33+...+361)-(1+3+32+...+360)
2S = 361 - 1
b,2S+1=361-1+1=361 = 3x-3
=>x-3=61=>x=64
c, S=1+3+32+...+360
=(1+3)+(32+33)+...+(359+360)
=4+32(1+3)+...+359(1+3)
=4+32.4+...+359.4
=4(1+32+...+359) chia hết cho 4
S=1+3+32+...+360
=(1+3+32)+....+(358+359+360)
=13+...+358(1+3+32)
=13+...+358.13
=13(1+...+358)
a, 720:[118-(2x -10) ]=60
[118-(2x-10)]=720:60
118-(2x-10)=12
2x-10=118-12
2x-10=106
2x =106+10
2x =116
x=116:2
x=58
\(a=3+3^2+3^3+...+3^{60}\)
\(a=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{59}+3^{60}\right)\)
\(a=3\left(1+3\right)+3^3\left(1+3\right)+...+3^{59}\left(1+3\right)\)
\(a=3.4+3^3.4+...+3^{59}.4\)
\(a=4\left(3+3^3+...+3^{59}\right)⋮4\left(đpcm\right)\)
( x + 1 ) ^3 - 4 = 60
= ( x + 1 ) ^3 = 60 + 4
= ( x + 1 ) ^3 = 64
= ( x + 1 ) ^3 = 4^3
= x + 1 = 4
= x = 4 - 1
= x = 3