Tìm số tự nhiên n biết:
\(\frac{1}{9}.27^n=3^n\)
\(3^{-2}.3^4.3^n=3^7\)
\(2^{-1}.2^n+4.2^n=9.2^5\)
\(32^{-n}.16^n=2048\)
Tìm x thuộc Z biết:
a) 2x+2-2x=96 b) 7x+2+2.7x-1=345 c) 3x-1+5.3x-1=162
Thu gọn tổng sau:
A=1+3+32+33+...+3100 B= 2100-299-298-297-...-22-2 C= 3100-399+398-397-...+32-3+1
2) a) 2x.(22 - 1) = 96 => 2x. 3 = 96 => 2x = 96 : 3 = 32 = 25 => x = 5
b) 7x. (72 + 2. 7-1) = 345 => 7x. \(\frac{345}{7}\) = 345 => 7x = 7 => x = 1
c) 3x-1. (1 + 5) = 162 => 3x-1 . 6 = 162 => 3x-1 = 162 : 6 = 27 = 33 => x - 1 = 3 => x = 3 + 1 = 4
1) a) (33)n = 9.3n => 33n = 32.3n = 32+n => 3n = 2 + n => 3n - n = 2 => 2n = 2 => n = 1
b) 3-2+4+n = 37 => 2 + n = 7 => n = 7 - 2 = 5
c) 2n.(2-1 + 4) = 9.25 => 2n.\(\frac{9}{2}\) = 9.25 => 2n-1 = 25 => n - 1 = 5 => n = 5 + 1 = 6
d) (25)-n.(24)n = 211 => 2-5n. 24n = 211 => 2-5n+4n = 211 => 2-n = 211 => -n = 11 => n = -11