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Bài 11 :

`a)  2^x . 4 = 128`

`2^x . 4= 128`

`2^x   = 128 : 4`

`2^x = 32`

`<=>2^x = 2^5`

`=> x = 5`

`b) 2^x - 26 = 6`

`2^x = 6 + 26`

`2^x = 32`

`<=> 2^x = 2^5`

`=> x = 5`

`c) 64.4^x= 4^5`

`4^3 .4^x= 4^5`

`4^3+x = 4^5`

`=> 3 +x = 5`

`x = 5-3`

`x = 2`

`d)`

`27.3^x = 243`

`3^3.3^x = 3^5`

`3^3+x = 3^5

`=>3 + x = 5`

`x = 5-2`

`x = 3`

`e ) 49.7^x = 2041 `

`<=> 7^(x+2) = 2401 = 7^4`
`<=> x + 2 = 4`
`<=> x =2`

`g ) 3^x = 81`

`<=> 3^x = 3^4`

`=> x = 4`

`h) `

`3^4.3^x = 3^7`

`3^x = 3^7 : 3^4 `

`3^x = 3^3`

`=>x = 3`

`k ) 3^x + 25 = 26.2^2 + 2.3^0`

`3^x+25=26 . 2^2 + 2. 3^0`

`3^x+25=104 +2`

`3^x+25=106`

`3^x=106+25`

`3^x=81=3^4`

`=> x=4        `

Bài 12 :

Ta có :` S = 1+2+2^2+2^3+..+2^100`

`2S = 2+2^2+2^4 + ..+2^101`

`2.S-S = (2+2^2+2^4 + ..+2^101) - (1+2+2^2+2^3+..+2^100 )`

`S = 2^100 -1