Toán Lớp 7: *Tìm số nguyên x, biết: a) `1/9` . $27^{n}$ = $3^{n}$ b) $3^{-2}$ . $3^{4}$ . $3^{n}$ = $3^{7}$ c) $2^{-1}$ . $2^{n}$ + 4 . $2^{n}$ =

Question

Toán Lớp 7:  *Tìm số nguyên x, biết: a) 1/9 . $27^{n}$ = $3^{n}$  b) $3^{-2}$ . $3^{4}$ . $3^{n}$ = $3^{7}$  c) $2^{-1}$ . $2^{n}$ + 4 . $2^{n}$ = 9 . $2^{5}$  d) $32^{-n}$ . $16^{n}$ = 2048

huongtructram · Answer

Giải đáp:    a, 1/9 . 27^n = 3^n   (3^3)^n : 3^2 = 3^n   3^(3n) : 3^2 = 3^n   3^(3n - 2) = 3^n   &rArr; 3n - 2 = n   &rArr; 3n - n = 2   2n         = 2              n = 1   b, 3^-2 . 3^4 . 3^n = 3^7   3^(-2 + 4 + n) = 3^7   3^(2 + n) = 3^7   &rArr; 2 + n = 7            n   = 7 - 2 = 5   c, 2^-1 + 2^n + 4 . 2^n = 9 . 2^5    2^n . (1/2 + 2) = 9 . 32   2^n . 9/2                     = 288   2^n                         =  288 : 9/2   2^n                         = 64   2^n                         = 2^6   &rArr; n                            = 6   d, 32^-n . 16^n = 2048   1/(32^n) . 16^n  = 2048   1/(2^n)               = 2048   1/(2^n)              = 2^11   &rArr; 2^n . 2^11 = 1    2^(n + 11) = 2^0   &rArr; n + 11 = 0    n             = 0 - 11 = -11

catlantuong · Answer

a,   1/9 . 27^n =3^n   1/3^2 . 3^(3.n)=3^n   3(3n-2)=3^n   ->  3n-2=n   ->   2n=2    ->  n=1   b,   3^-2 . 3^4 . 3^n =3^7   ->  3^(-2+4+n)=3^7   ->   3^(n+2)=3^7   ->    n+2=7   ->     n=5   c,   2^-1 .2^n + 4.2^n=9.2^5   ->   1/2 .2^n + 4.2^n=3^2 .2^5   ->     2^n.(1/2 +4)=3^2 .2^5   ->      2^n . 9/2 =3^2 .2^5   ->      2^(n-1) .9 =9 .2^5   ->           n-1=5   ->            n=6   d,   32^-n .16^n =2048   ->   1/32^n .16^n =2^11   ->     1/(2^(5.n))   . 2^(4.n)=2^11   ->      1/2^n = 2^11   ->       2^n . 2^11=1=2^0   ->         n+11=0   ->           n=-11