Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Trong b\u00e0i h\u1ecdc l\u1ea7n tr\u01b0\u1edbc, c\u00e1c b\u1ea1n nh\u1ecf \u0111\u00e3 c\u0169ng Vietlearn l\u00e0m quen v\u1ec1 l\u0169y th\u1eeba, bi\u1ebft c\u00e1ch vi\u1ebft v\u00e0 t\u00ednh to\u00e1n ph\u00e9p t\u00ednh nh\u00e2n hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1. B\u00e0i gi\u1ea3ng h\u00f4m nay, ch\u00fang ta s\u1ebd ti\u1ebfp t\u1ee5c h\u1ecdc v\u1ec1 ph\u00e9p t\u00ednh chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1.<\/p>\n\n\n\n
L\u00fd thuy\u1ebft chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1<\/p>\n\n\n\n
C\u00f4ng th\u1ee9c ph\u00e9p chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1<\/p>\n\n\n\n
L\u01b0u \u00fd: Khi th\u1ea5y c\u01a1 s\u1ed1 kh\u00f4ng vi\u1ebft s\u1ed1 m\u0169, ta m\u1eb7c \u0111\u1ecbnh \u0111\u00f3 l\u00e0 c\u01a1 s\u1ed1 l\u0169y th\u1eeba 1 (a = a^0 = 1, a \u2260 0). Ta c\u00f3: a^m : a = a^m-1.<\/p>\n\n\n\n
V\u00ed d\u1ee5: 8^4 : 8 = 8^4-1 = 8^3<\/p>\n\n\n\n
H\u01b0\u1edbng gi\u1ea3i m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 SGK<\/p>\n\n\n\n
B\u00e0i t\u1eadp 67 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
Gi\u1ea3i b\u00e0i t\u1eadp 67 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i t\u1eadp 68 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
C\u00e1ch 1:<\/p>\n\n\n\n
C\u00e1ch 1 (Gi\u1ea3i b\u00e0i t\u1eadp 68, trang 30 SGK)<\/p>\n\n\n\n
C\u00e1ch 2:<\/p>\n\n\n\n
C\u00e1ch 2 (Gi\u1ea3i b\u00e0i t\u1eadp 68, trang 30 SGK)<\/p>\n\n\n\n
B\u00e0i t\u1eadp 69 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i t\u1eadp 69 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
B\u00e0i t\u1eadp 70 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
Gi\u1ea3i b\u00e0i t\u1eadp 70 (trang 30, SGK To\u00e1n l\u1edbp 6 t\u1eadp 1)<\/p>\n\n\n\n
T\u1ea3i b\u1ed9 t\u00e0i li\u1ec7u v\u00e0 \u0111\u1ec1 thi Full m\u00f4n h\u1ecdc tuy\u1ec7t hay (c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft)<\/p><\/blockquote>\n\n\n\n
B\u00e0i t\u1eadp luy\u1ec7n t\u1eadp chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 (B\u1ed5 sung)<\/p>\n\n\n\n
\u0110\u1ec1 b\u00e0i<\/p>\n\n\n\n
B\u00e0i t\u1eadp 1. Vi\u1ebft k\u1ebft qu\u1ea3 m\u1ed7i ph\u00e9p t\u00ednh sau d\u01b0\u1edbi d\u1ea1ng m\u1ed9t l\u0169y th\u1eeba:<\/p>\n\n\n\n
a. 6^7 : 6^5<\/p>\n\n\n\n
b. 9^5 : 9^4<\/p>\n\n\n\n
7^5 : 7^5<\/p>\n\n\n\n
2^4 : 2<\/p>\n\n\n\n
5^6 : 5^5<\/p>\n\n\n\n
3^4 : 3^2<\/p>\n\n\n\n
6^5 : 6^5<\/p>\n\n\n\n
4^2 : 4<\/p>\n\n\n\n
B\u00e0i t\u1eadp 2. T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean b bi\u1ebft r\u1eb1ng v\u1edbi m\u1ecdi n \u2208 N* ta c\u00f3:<\/p>\n\n\n\n
b^n = 2<\/p>\n\n\n\n
b^n = 3<\/p>\n\n\n\n
b^n = 4<\/p>\n\n\n\n
B\u00e0i t\u1eadp 3: Vi\u1ebft c\u00e1c s\u1ed1: 234; 4567; 23456 d\u01b0\u1edbi d\u1ea1ng t\u1ed5ng c\u00e1c l\u0169y th\u1eeba c\u1ee7a 10<\/p>\n\n\n\n
B\u00e0i t\u1eadp 4: T\u00ecm gi\u00e1 tr\u1ecb x th\u1ecfa m\u00e3n:<\/p>\n\n\n\n
6^x : 6^3 = 6^11<\/p>\n\n\n\n
13^25 : 13^x = 13^4<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i b\u00e0i t\u1eadp 1<\/p>\n\n\n\n
\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c: a^m : a^n = a^m-n (a \u2260 0, m \u2265 n)<\/p>\n\n\n\n
Ta c\u00f3:<\/p>\n\n\n\n
6^7 : 6^5 = 6^7-5 = 6^2<\/p>\n\n\n\n
9^5 : 9^4 = 9^5-4 = 9<\/p>\n\n\n\n
7^5 : 7^5 = 7^5-5 = 7^0 = 1<\/p>\n\n\n\n
2^4 : 2 = 2^4-1 = 2^3<\/p>\n\n\n\n
5^6 : 5^5 = 5^6-5 = 5<\/p>\n\n\n\n
3^4 : 3^2 = 3^4-2 = 3^2<\/p>\n\n\n\n
6^5 : 6^5 = 6^5-5 = 6^0 = 1<\/p>\n\n\n\n
4^2 : 4 = 4^2-1 = 4<\/p>\n\n\n\n
B\u00e0i t\u1eadp 2:<\/p>\n\n\n\n
Ta c\u00f3:<\/p>\n\n\n\n
b^n = 2 => n = 2<\/p>\n\n\n\n
b^n = 3 => n = 3<\/p>\n\n\n\n
b^n = 4 => n = 4<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i b\u00e0i t\u1eadp 2 chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1<\/p>\n\n\n\n
B\u00e0i t\u1eadp 3:<\/p>\n\n\n\n
Ta c\u00f3:<\/p>\n\n\n\n
234 = 2.100 + 3.10 + 4<\/p>\n\n\n\n
= 2.10^2 + 3.10^1 + 4.10^0<\/code><\/pre>\n\n\n\n4567 = 4.1000 + 5.100 + 6.10 + 7<\/p>\n\n\n\n
= 4.10^3 + 5.10^2 + 6^10^1 + 7^10^0<\/code><\/pre>\n\n\n\n23456 = 2.10000 + 3.1000 + 4.100 + 5.10 + 6<\/p>\n\n\n\n
= 2.10^4 + 3.10^3 + 4^10^2 + 5.10^1 + 6.10^0<\/code><\/pre>\n\n\n\nL\u1eddi gi\u1ea3i b\u00e0i t\u1eadp 3<\/p>\n\n\n\n
B\u00e0i t\u1eadp 4:<\/p>\n\n\n\n
Ta c\u00f3:<\/p>\n\n\n\n
6^x : 6^3 = 6^11<\/p>\n\n\n\n
\u21d4 6^x-3 = 6^11<\/p>\n\n\n\n
\u21d4 x-3 = 11<\/p>\n\n\n\n
\u21d4 x = 11 + 4<\/p>\n\n\n\n
\u21d4 x = 14<\/p>\n\n\n\n
V\u1eady x = 14<\/p>\n\n\n\n
b. Ta c\u00f3:<\/code><\/pre>\n\n\n\n13^25 : 13^x = 13^4<\/p>\n\n\n\n
\u21d4 13^25-x = 13^4<\/p>\n\n\n\n
\u21d4 25-x = 4<\/p>\n\n\n\n
\u21d4 x = 25 \u2013 4<\/p>\n\n\n\n
\u21d4 x = 21<\/p>\n\n\n\n
V\u1eady x = 21<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i b\u00e0i t\u1eadp 4<\/p>\n\n\n\n
B\u1ed5 sung ki\u1ebfn th\u1ee9c to\u00e1n l\u1edbp 6 chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1<\/p>\n\n\n\n
Kh\u00e1i ni\u1ec7m l\u0169y th\u1eeba<\/p>\n\n\n\n
L\u0169y th\u1eeba l\u00e0 ph\u00e9p to\u00e1n to\u00e1n h\u1ecdc, \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng \u201ca^n\u201d, bao g\u1ed3m ch\u1eef s\u1ed1, c\u01a1 s\u1ed1 \u201ca\u201d v\u00e0 s\u1ed1 m\u0169 n (l\u0169y th\u1eeba). Ph\u00e9p t\u00ednh \u0111\u01b0\u1ee3c ph\u00e1t \u00e2m l\u00e0 \u201ca\u201d m\u0169 \u201cn\u201d hay a l\u0169y th\u1eeba \u201cn\u201d.<\/p>\n\n\n\n
Khi l\u0169y th\u1eeba \u201cn\u201d l\u00e0 s\u1ed1 nguy\u00ean d\u01b0\u01a1ng, t\u01b0\u01a1ng \u1ee9ng v\u1edbi ph\u00e9p nh\u00e2n l\u1eb7p c\u1ee7a c\u01a1 s\u1ed1 \u201ca\u201d, \u201ca^n\u201d l\u00e0 t\u00edch c\u1ee7a ph\u00e9p nh\u00e2n \u201cn\u201d c\u01a1 s\u1ed1.<\/p>\n\n\n\n
Ta c\u00f3:<\/p>\n\n\n\n
a^n = {a.a.a.a\u2026a} (n l\u00e0 th\u1eeba s\u1ed1 c\u1ee7a a)<\/p>\n\n\n\n
V\u00ed d\u1ee5: a^4 = a x a x a x a<\/p>\n\n\n\n
C\u00e1c ph\u00e9p t\u00ednh l\u0169y th\u1eeba l\u1edbp 6 c\u1ea7n nh\u1edb<\/p>\n\n\n\n
L\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 t\u1ef1 nhi\u00ean: a^n = {a.a.a.a\u2026a} (n l\u00e0 th\u1eeba s\u1ed1 c\u1ee7a a)<\/p>\n\n\n\n
Nh\u00e2n hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1: a^m . a^n = a^m+n<\/p>\n\n\n\n
Chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1: a^m : a^n = a^m-n (a \u2260 0, m \u2265 n)<\/p>\n\n\n\n
L\u0169y th\u1eeba c\u1ee7a l\u0169y th\u1eeba: (a^m)^n = a^m.n<\/p>\n\n\n\n
Nh\u00e2n hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169, kh\u00e1c c\u01a1 s\u1ed1: a^m . b^m = (a.b)^m<\/p>\n\n\n\n
Chia hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169, kh\u00e1c c\u01a1 s\u1ed1: a^m : b^m = (a:b)^m<\/p>\n\n\n\n
M\u1ed9t s\u1ed1 l\u01b0u \u00fd gi\u1ea3i b\u00e0i t\u1eadp luy\u1ec7n t\u1eadp<\/p>\n\n\n\n
Kho t\u00e0i li\u1ec7u h\u1ecdc t\u1eadp<\/a> Mi\u1ec5n Ph\u00ed \u2013 Vietlearn<\/p>\n\n\n\n
To\u00e1n l\u1edbp 6 chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 l\u00e0 ph\u00e9p t\u00ednh to\u00e0n to\u00e1n h\u1ecdc nh\u00ecn c\u00f3 v\u1ebb \u0111\u01a1n gi\u1ea3n v\u00e0 nh\u1eb9 nh\u00e0ng. Nh\u01b0ng \u0111\u00e2y l\u1ea1i l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng v\u00e0 quan tr\u1ecdng \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp ph\u01b0\u01a1ng tr\u00ecnh \u0111a b\u1eadc v\u00e0 c\u0103n b\u1eadc sau n\u00e0y. Do \u0111\u00f3, \u0111\u1eebng v\u1ed9i v\u00e0ng coi nh\u1eb9 ki\u1ebfn th\u1ee9c c\u1ee7a ph\u00e9p t\u00ednh to\u00e1n n\u00e0y.<\/p>\n\n\n\n
B\u00e9 c\u1ea7n ph\u1ea3i n\u1eafm ch\u1eafc ki\u1ebfn th\u1ee9c c\u1ed9ng, tr\u1eeb, nh\u00e2n, chia tr\u01b0\u1edbc khi ti\u1ebfn h\u00e0nh gi\u1ea3i b\u00e0i t\u1eadp chia l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1.<\/p>\n\n\n\n
Lu\u00f4n nh\u1edb \u0111i\u1ec1u ki\u1ec7n v\u00e0 quy \u01b0\u1edbc chung khi gi\u1ea3i b\u00e0i t\u1eadp.<\/p>\n\n\n\n
Kh\u00f4ng ch\u1ee7 quan, h\u1ea1n ch\u1ebf gi\u1ea3i t\u1eaft v\u00e0 c\u1ea9n th\u1eadn gi\u1ea3i b\u00e0i t\u1eadp t\u1eebng b\u01b0\u1edbc m\u1ed9t \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o k\u1ebft qu\u1ea3 ch\u00ednh x\u00e1c nh\u1ea5t v\u00e0 n\u1eafm r\u00f5 c\u00e1c b\u01b0\u1edbc gi\u1ea3i.<\/p>\n\n\n\n
C\u00e1c b\u00e0i gi\u1ea3i m\u1eabu ch\u1ec9 mang t\u00ednh ch\u1ea5t tham kh\u1ea3o. H\u1ea1n ch\u1ebf d\u1ef1a d\u1eabm v\u00e0o c\u00e1c b\u00e0i gi\u1ea3i m\u1eabu khi l\u00e0m b\u00e0i t\u1eadp. R\u00e8n luy\u1ec7n kh\u1ea3 n\u0103ng v\u00e0 tinh th\u1ea7n t\u1ef1 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n.<\/p>\n\n\n\n
Kh\u00f3a h\u1ecdc gia<\/a> s\u01b0 Online Vietlearn gi\u00fap c\u00e1c em d\u1ec5 d\u00e0ng n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c m\u00f4n To\u00e1n l\u1edbp 6.<\/p>\n\n\n\n
Gi\u1edbi thi\u1ec7u Vietlearn Education<\/p>\n\n\n\n
Vietlearn \u2013 Kh\u00f3a h\u1ecdc gia<\/a> s\u01b0 To\u00e1n tr\u1ef1c tuy\u1ebfn s\u1ed1 1 Vi\u1ec7t Nam<\/p>\n\n\n\n
Vietlearn l\u00e0 c\u00f4ng ty Edtech v\u1ec1 gi\u00e1o d\u1ee5c tr\u1ef1c tuy\u1ebfn, cung c\u1ea5p tr\u1ea3i nghi\u1ec7m v\u00e0 b\u1ed3i d\u01b0\u1ee1ng h\u1ecdc t\u1eadp<\/a> c\u00e1 nh\u00e2n cho h\u00e0ng tr\u0103m ngh\u00ecn h\u1ecdc sinh<\/a> v\u00e0 nh\u00e0 tr\u01b0\u1eddng trong kh\u1ed1i ki\u1ebfn th\u1ee9c K-12 c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh gi\u00e1o d\u1ee5c.<\/p>\n\n\n\n
Vietlearn kh\u00f4ng ch\u1ec9 l\u00e0 kh\u00f3a h\u1ecdc To\u00e1n, ch\u00fang t\u00f4i \u1ee9ng d\u1ee5ng v\u00e0 mang \u0111\u1ebfn tr\u1ea3i nghi\u1ec7m tri th\u1ee9c tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o (AI) v\u00e0 d\u1eef li\u1ec7u l\u1edbn (h\u00e0ng \u0111\u1ea7u \u0110\u00f4ng Nam \u00c1) \u0111\u1ebfn v\u1edbi c\u00e1c b\u1ea1n nh\u1ecf. Vietlearn mong mu\u1ed1n t\u1ea1o ra m\u00f4i tr\u01b0\u1eddng c\u00f4ng ngh\u1ec7 gi\u00fap c\u00e1c em ph\u00e1t huy \u0111i\u1ec3m m\u1ea1nh v\u00e0 say m\u00ea trong h\u1ecdc t\u1eadp.<\/p>\n\n\n\n
B\u1ed3i d\u01b0\u1ee1ng, truy\u1ec1n c\u1ea3m h\u1ee9ng v\u00e0 truy\u1ec1n l\u1eeda h\u1ecdc t\u1eadp cho th\u1ebf h\u1ec7 tr\u1ebb lu\u00f4n l\u00e0 s\u1ee9 m\u1ec7nh c\u1ed1t l\u00f5i kh\u00f4ng thay \u0111\u1ed5i c\u1ee7a Vietlearn.<\/p>\n\n\n\n
M\u00f4 h\u00ecnh gi\u00e1o d\u1ee5c v\u00e0 \u0111\u1ed9i ng\u0169 gi\u00e1o vi\u00ean c\u1ee7a Vietlearn \u0111\u01b0\u1ee3c nhi\u1ec1u t\u1ed5 ch\u1ee9c v\u00e0 c\u01a1 quan b\u00e1o ch\u00ed \u0111\u00e1nh gi\u00e1 ch\u1ea5t l\u01b0\u1ee3ng h\u00e0ng \u0111\u1ea7u Vi\u1ec7t Nam.<\/p>\n\n\n\n
Tr\u00ean \u0111\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c \u201cchia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1\u201d, hy v\u1ecdng \u0111\u00e3 gi\u00fap c\u00e1c b\u1ea1n nh\u1ecf hi\u1ec3u v\u00e0 ho\u00e0n th\u00e0nh t\u1ed1t c\u00e1c b\u00e0i t\u1eadp \u1edf tr\u00ean l\u1edbp v\u00e0 c\u1ee7a Vietlearn.<\/p>\n\n\n\n
<\/p>\n\n\n\n
L\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 t\u1ef1 nhi\u00ean. Nh\u00e2n hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1<\/p>\n\n\n\n
Th\u1ee9<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Trong b\u00e0i h\u1ecdc l\u1ea7n tr\u01b0\u1edbc, c\u00e1c b\u1ea1n nh\u1ecf \u0111\u00e3 c\u0169ng Vietlearn l\u00e0m quen v\u1ec1 l\u0169y th\u1eeba, bi\u1ebft c\u00e1ch vi\u1ebft v\u00e0 t\u00ednh to\u00e1n ph\u00e9p t\u00ednh nh\u00e2n hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1. B\u00e0i gi\u1ea3ng h\u00f4m nay, ch\u00fang ta s\u1ebd ti\u1ebfp t\u1ee5c h\u1ecdc v\u1ec1 ph\u00e9p t\u00ednh chia hai l\u0169y th\u1eeba c\u00f9ng […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9,4],"tags":[],"class_list":["post-2497","post","type-post","status-publish","format-standard","hentry","category-toan-hoc","category-trung-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/2497","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=2497"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/2497\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=2497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=2497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=2497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}