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thay 11=x+1 ta có:
f(x)= \(x^{10}\)-11\(x^9\)+11\(x^8\)-11\(x^7\)+....+11\(x^2\)-11x+100
=\(x^{10}\)-(x+1)\(x^9\)+(x+1)\(x^8\)-(x+1)\(x^7\)+...+(x+1)\(x^2\)-(x+1)x+100
=\(x^{10}\)-\(x^{10}\)-\(x^9\)+\(x^9\)+\(x^8\)-\(x^8\)-\(x^7\)+......+\(x^3\)+\(x^2\)-\(x^2\)-x+100
=-x+100
=> f(10)=-10+100=90
Thay 11 = x + 1 ta có:
f(x) = \(x^{10}-11x^9+11x^8-11x^7+...+11x^2-11x+100\)
\(=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-\left(x+1\right)x^7+...+\left(x+1\right)x^2-\left(x+1\right)x^2-\left(x+1\right)x+100\)
= \(x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^3+x^2-x^2-x+100\)
= -x+100
=>f(10)= - 10 + 100 = 90
a, Tự chép đề bài :v
=> 22x-3 = ( 83. 165 ) : 410
22x-3 = ( 29. 220 ) : 220
22x-3 = 229 : 220
22x-3 = 29
=> 2x - 3 = 9
2x = 9 + 3
2x = 12
x = 6
Vậy....
b, 7. 2x = 29 + 5. 28
7. 2x = 1792
2x = 1792 : 7
2x = 256
2x = 28
=> x = 8
Vậy ....
a \(\frac{2^{2x-3}}{4^{10}}=8^3.16^5\)
\(\Leftrightarrow\frac{2^{2x-3}}{4^{10}}=2^{29}\)
\(\Leftrightarrow2^{2x-3}=2^{29}.4^{10}\)
\(\Leftrightarrow2^{2x-3}=2^{49}\)
\(\Leftrightarrow2x-3=49\)
\(\Leftrightarrow x=26\)
b \(7.2^x=2^9+5.2^8\)
\(\Leftrightarrow7.2^x=2^8.(2+5)\)
\(\Leftrightarrow7.2^x=7.2^8\)
\(\Leftrightarrow x=7\)
a/ 72+x + 2.7x-1 =345
73 . 7x-1 + 2.7x-1 = 345
7x-1 (73+2) = 345
7x-1 . 345 = 345
7x-1 = 345 : 345 = 1
7x-1 = 70
x - 1 = 0
x = 0+1 = 1
b/ 81-2x . 27x = 95
(34)-2x . (33)x = (32)5
34.(-2x) . 33.x = 32.5
3-8x . 33x = 310
3-8x+3x = 310
3-5x = 310
-5x = 10
x = 10 : (-5) = -2
Bài 1 :
\(8^7-2^{18}\)
\(=\left(2^3\right)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{18}\left(2^3-1\right)\)
\(=2^{18}\cdot7\)
\(=2^{17}\cdot2\cdot7\)
\(=2^{17}\cdot14⋮14\left(đpcm\right)\)
2x+2-2x=96
=>2x.(22-1)=96
=>2x.3=96
=>2x=32
=>2x=25
=>x=5
7.2x=29+5.28
=>7.2x=28.(2+5)=
=>7.2x=28.7
=>2x=28
=>x=8