~Bạn tham khảo~
Bài `1:`
`a)(x-5)^4 = 4^2`
`=>(x-5)^4 =(2^2 )^2`
`=>(x-5)^4 = 2^4`
`=>x-5=2`
`=>x=7`
Vậy `x=7`
`b)2^(2x).2^x =1024`
`=>2^(3x)=1024`
`=>2^(3x) = 2^10`
`=>3x=10`
`=>x=10/3`
Vậy `x=10/3`
`c)` Sửa đề : `2^(x+3) + 2^x = 9.64`
`=>2^x . 8+2^x = 576`
`=>2^x (8+1) =576`
`=>2^x . 9=576`
`=>2^x =64`
`=>2^x = 2^6`
`=>x=6`
Vậy `x-6`
`d)(19x +25^2 ) : 14=(13-8)^2 -4^2`
`=>(19x+ 625):14 = 5^2 - 16`
`=>(19x+625):14=25-16`
`=>(19x+625):14=9`
`=>19x+625=126`
`=>19x=126-625`
`=>19x=-499`
`=>x=(-499)/19`
Vậy `x=(-499)/19`
Bài `2` :
`a)A=1+4+4^2 + 4^3 + 4^4 + ... + 4^100`
`=>4A=4+4^2 + 4^3 + 4^4 +4^5 + ... + 4^101`
`=>4A-A=(4+4^2 + 4^3 + 4^4 +4^5 + ... + 4^101 )-(1+4+4^2 + 4^3 + 4^4 + ... + 4^100 )`
`=>3A=4^101 -1`
`=>A=(4^101 -1)/3`
`b)` Sửa đề : `B=1+3+3^2+3^3 +...+3^1000`
`=>3B=3+3^2+3^3 +3^4 +...+3^1001`
`=>3B-B = ( 3+3^2+3^3 +3^4 +...+3^1001 )-(1+3+3^2+3^3 +...+3^1000)`
`=>3B=3^1001 - 1`
`=>B=(3^1001 - 1)/3`
