BẠN ƠI VIẾT SỐ MŨ NHƯ NÀO VẬY BẠN

Ta có:\(1+4^1+4^2+4^3+....+4^{58}+4^{59}\)

\(=4^0+4^1+4^2+4^3+....+4^{58}+4^{59}\)

\(=\left(4^0+4^1+4^2\right)+\left(4^3+4^4+4^5\right)+.....+\left(4^{57}+4^{58}+4^{59}\right)\)

\(=21+\left[4.\left(1+4+4^2\right)\right]+....+\left[4^{57}.\left(1+4+4^2\right)\right]\)

\(=21+4.21+.....+4^{57}.21\)

\(=21.\left(1+4+......+4^{57}\right)⋮21\)

\(D=5+5\cdot9+5\cdot9^2+....+5\cdot9^{99}.\)

\(=5\cdot\left(1+9+9^2+....+9^{99}\right)\)

Gọi \(E=\left(1+9+9^2+....+9^{99}\right)\)

\(\Rightarrow9E=9+9^2+9^3+...+9^{100}\)

\(9E-E=\left(9+9^2+9^3+....+9^{100}\right)-\left(1+9+9^2+....+9^{99}\right)\)

\(8E=9^{100}-1\)

\(\Rightarrow E=\frac{9^{100}-1}{8}\)

\(\Rightarrow D=5\cdot\left(1+9+9^2+....+9^{99}\right)=5\cdot\frac{9^{100}-1}{8}\)

D = 5 * [9¹⁰⁰ * 9]

 B = 1 + 2 + 2² + 2³ +....+ 2³²

2B = 2 + 2² + 2³ + 2⁴ +....+ 2³³

2B - B = 2³³ - 1

\(\Rightarrow\)B < A Vì 2³³ - 1 < 2³³

Hk tốt

\(B=1+2+2^2+2^3+....+2^{32}\)

\(\Rightarrow2B=2+2^2+2^3+2^4+....+2^{33}\)

\(2B-B=\left(2+2^2+2^3+2^4+....+2^{33}\right)-\left(1+2+2^2+2^3+....+2^{32}\right)\)

\(B=2^{33}-1< 2^{33}\)

Vậy \(B< A\)

(x-5)³=8

(x-5)³=2³

x-5=2(vì số mũ 3>0)

x=7

\(a.2^x=32\Leftrightarrow2^x=2^5\Leftrightarrow x=5\)

\(b.\left(x-5\right)^3=8\Leftrightarrow\left(x-5\right)^3=2^3\Leftrightarrow x-5=2\Leftrightarrow x=7\)

\(c.5^{x+1}=25\Leftrightarrow5^{x+1}=5^2\Leftrightarrow x+1=2\Leftrightarrow x=1\)

\(d.3\cdot\left(6x+3\right)=3^5\)

\(\Leftrightarrow6x+3=3^4\)

\(\Leftrightarrow6x=3^4-3=81-3=78\)

\(\Leftrightarrow x=78:613\)

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Ta có : \(432=2^4.3^3\)

             \(720=2^4.3^2.5\)

ƯCLN(432;720) = 2⁴ .3²   = 144

ƯC(432;720) ={ 1;2;3;4;...;144}

Ta có :

432 = 2⁴ . 3³

720 = 2⁴ . 3² . 5

ƯCLN ( 432; 720 ) = 2⁴ . 3² = 144

ƯC ( 432 ; 720 ) = Ư( 144) = { 1; 2; 3; 4; 8; 9; 12; 16; 18; 36; 72; 144 }