Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Mon, 13 May 2024 17:00:00 +0000 vi hourly 1 https://wordpress.org/?v=7.1.3 Cho \(a,\,b,\,c\) là các số thực dương và khác \(1\) thỏa mãn \(\log _a^2b + \log _b^2c + 2{\log _b}\frac{c}{b} = {\log _a}\frac{c}{{{a^3}b}}\). Gọi \(M,m\) lần lượt là giá trị lớn nhất và giá trị nhỏ nhất của \(P = {\log _a}\left( {ab} \right) – {\log _b}\left( {bc} \right)\). Tính giá trị biểu thức \(S = 2{m^2} + 9{M^2}\). https://booktoan.com/cho-abc-la-cac-so-thuc-duong-va-khac-1-thoa-man-log-_a2b-log-_b2c-2log-_bfraccb-log-_afracca3b-goi-mm-lan-luot-la-gia-tri-lon-nha.html https://booktoan.com/cho-abc-la-cac-so-thuc-duong-va-khac-1-thoa-man-log-_a2b-log-_b2c-2log-_bfraccb-log-_afracca3b-goi-mm-lan-luot-la-gia-tri-lon-nha.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-abc-la-cac-so-thuc-duong-va-khac-1-thoa-man-log-_a2b-log-_b2c-2log-_bfraccb-log-_afracca3b-goi-mm-lan-luot-la-gia-tri-lon-nha.html https://booktoan.com/cho-abc-la-cac-so-thuc-duong-va-khac-1-thoa-man-log-_a2b-log-_b2c-2log-_bfraccb-log-_afracca3b-goi-mm-lan-luot-la-gia-tri-lon-nha.html/feed 0 Cho các số thực dương \(a \ne 1,\,b \ne 1\) thỏa mãn \({\log _3}a = {\log _b}81\) và tích \(ab = 729\). Tính giá trị của biểu thức \({\left( {{{\log }_3}\frac{a}{b}} \right)^2}\). https://booktoan.com/cho-cac-so-thuc-duong-a-ne-1b-ne-1-thoa-man-log-_3a-log-_b81-va-tich-ab-729-tinh-gia-tri-cua-bieu-thuc-left-log-_3fracab-right2.html https://booktoan.com/cho-cac-so-thuc-duong-a-ne-1b-ne-1-thoa-man-log-_3a-log-_b81-va-tich-ab-729-tinh-gia-tri-cua-bieu-thuc-left-log-_3fracab-right2.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-cac-so-thuc-duong-a-ne-1b-ne-1-thoa-man-log-_3a-log-_b81-va-tich-ab-729-tinh-gia-tri-cua-bieu-thuc-left-log-_3fracab-right2.html https://booktoan.com/cho-cac-so-thuc-duong-a-ne-1b-ne-1-thoa-man-log-_3a-log-_b81-va-tich-ab-729-tinh-gia-tri-cua-bieu-thuc-left-log-_3fracab-right2.html/feed 0 Cho \(a\) và \(b\) là hai số thực dương phân biệt, khác 1 và thỏa mãn \(\log _a^2\left( {{a^3}b} \right).{\log _{\sqrt a }}\frac{{\sqrt {{b^3}} }}{a} – 100 = 0\). Giá trị của \({\log _b}a\) bằng https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-khac-1-va-thoa-man-log-_a2left-a3b-right-log-_sqrt-a-fracsqrt-b3-a-100-0-gia-tri-cua-log-_b.html https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-khac-1-va-thoa-man-log-_a2left-a3b-right-log-_sqrt-a-fracsqrt-b3-a-100-0-gia-tri-cua-log-_b.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-khac-1-va-thoa-man-log-_a2left-a3b-right-log-_sqrt-a-fracsqrt-b3-a-100-0-gia-tri-cua-log-_b.html https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-khac-1-va-thoa-man-log-_a2left-a3b-right-log-_sqrt-a-fracsqrt-b3-a-100-0-gia-tri-cua-log-_b.html/feed 0  Cho các số \(a,b > 0\) thỏa mãn \(3 + {\log _3}a = 5 + {\log _5}b = {\log _{15}}(a + b)\). Tính giá trị của biểu thức \(\frac{1}{a} + \frac{1}{b}\). https://booktoan.com/cho-cac-so-ab-0-thoa-man-3-log-_3a-5-log-_5b-log-_15a-b-tinh-gia-tri-cua-bieu-thuc-frac1a-frac1b.html https://booktoan.com/cho-cac-so-ab-0-thoa-man-3-log-_3a-5-log-_5b-log-_15a-b-tinh-gia-tri-cua-bieu-thuc-frac1a-frac1b.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-cac-so-ab-0-thoa-man-3-log-_3a-5-log-_5b-log-_15a-b-tinh-gia-tri-cua-bieu-thuc-frac1a-frac1b.html https://booktoan.com/cho-cac-so-ab-0-thoa-man-3-log-_3a-5-log-_5b-log-_15a-b-tinh-gia-tri-cua-bieu-thuc-frac1a-frac1b.html/feed 0 nbsp; Có bao nhiêu cặp số dương \(a,\,\,b\) thỏa mãn \({\log _2}a\) và \({\log _2}b\) là các số nguyên, đồng thời\(\left( {{{\log }_2}ab – 11} \right).{\log _2}\frac{{{a^2}}}{b} = 3\)? https://booktoan.com/nbsp-co-bao-nhieu-cap-so-duong-ab-thoa-man-log-_2a-va-log-_2b-la-cac-so-nguyen-dong-thoileft-log-_2ab-11-right-log-_2fraca2b-3.html https://booktoan.com/nbsp-co-bao-nhieu-cap-so-duong-ab-thoa-man-log-_2a-va-log-_2b-la-cac-so-nguyen-dong-thoileft-log-_2ab-11-right-log-_2fraca2b-3.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/nbsp-co-bao-nhieu-cap-so-duong-ab-thoa-man-log-_2a-va-log-_2b-la-cac-so-nguyen-dong-thoileft-log-_2ab-11-right-log-_2fraca2b-3.html https://booktoan.com/nbsp-co-bao-nhieu-cap-so-duong-ab-thoa-man-log-_2a-va-log-_2b-la-cac-so-nguyen-dong-thoileft-log-_2ab-11-right-log-_2fraca2b-3.html/feed 0 Có bao nhiêu cặp số nguyên \(\left( {a\,;\,\,b} \right)\) thoả mãn \({\log _2}\left( {{3^{{a^2}}} + 1} \right) + {b^2} – 3b \le 0\)? https://booktoan.com/co-bao-nhieu-cap-so-nguyen-left-ab-right-thoa-man-log-_2left-3a2-1-right-b2-3b-le-0.html https://booktoan.com/co-bao-nhieu-cap-so-nguyen-left-ab-right-thoa-man-log-_2left-3a2-1-right-b2-3b-le-0.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/co-bao-nhieu-cap-so-nguyen-left-ab-right-thoa-man-log-_2left-3a2-1-right-b2-3b-le-0.html https://booktoan.com/co-bao-nhieu-cap-so-nguyen-left-ab-right-thoa-man-log-_2left-3a2-1-right-b2-3b-le-0.html/feed 0 Cho \(a,\,b\) là các số thực thỏa mãn \(0 < a < 1 < b\) và \({\log _a}\frac{b}{{{a^4}}}.{\log _{a{b^2}}}a + {\log _{\sqrt a }}b + 2 = 0\). Giá trị của \({\log _a}b\) bằng https://booktoan.com/cho-ab-la-cac-so-thuc-thoa-man-0-a-1-b-va-log-_afracba4-log-_ab2a-log-_sqrt-a-b-2-0-gia-tri-cua-log-_ab-bang.html https://booktoan.com/cho-ab-la-cac-so-thuc-thoa-man-0-a-1-b-va-log-_afracba4-log-_ab2a-log-_sqrt-a-b-2-0-gia-tri-cua-log-_ab-bang.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-ab-la-cac-so-thuc-thoa-man-0-a-1-b-va-log-_afracba4-log-_ab2a-log-_sqrt-a-b-2-0-gia-tri-cua-log-_ab-bang.html https://booktoan.com/cho-ab-la-cac-so-thuc-thoa-man-0-a-1-b-va-log-_afracba4-log-_ab2a-log-_sqrt-a-b-2-0-gia-tri-cua-log-_ab-bang.html/feed 0  Cho \(a > 0,b > 0,{a^2}b \ne 1,a{b^2} \ne 1\) và \({\log _{{a^2}b}}\left( {\frac{{a{b^3}}}{{\sqrt {ab} }}} \right) = \frac{8}{5}\). Tính \({\log _{a{b^2}}}b\). https://booktoan.com/cho-a-0b-0a2b-ne-1ab2-ne-1-va-log-_a2bleft-fracab3sqrt-ab-right-frac85-tinh-log-_ab2b.html https://booktoan.com/cho-a-0b-0a2b-ne-1ab2-ne-1-va-log-_a2bleft-fracab3sqrt-ab-right-frac85-tinh-log-_ab2b.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-a-0b-0a2b-ne-1ab2-ne-1-va-log-_a2bleft-fracab3sqrt-ab-right-frac85-tinh-log-_ab2b.html https://booktoan.com/cho-a-0b-0a2b-ne-1ab2-ne-1-va-log-_a2bleft-fracab3sqrt-ab-right-frac85-tinh-log-_ab2b.html/feed 0 Cho \(a\) và \(b\) là hai số thực dương phân biệt, \(a\) khác 1 và thoả mãn \({a^{\log _a^2b}} + {b^{{{\log }_a}b}} = 2b\). Giá trị của \({\log _a}b\) bằng https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-a-khac-1-va-thoa-man-alog-_a2b-blog-_ab-2b-gia-tri-cua-log-_ab-bang.html https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-a-khac-1-va-thoa-man-alog-_a2b-blog-_ab-2b-gia-tri-cua-log-_ab-bang.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-a-khac-1-va-thoa-man-alog-_a2b-blog-_ab-2b-gia-tri-cua-log-_ab-bang.html https://booktoan.com/cho-a-va-b-la-hai-so-thuc-duong-phan-biet-a-khac-1-va-thoa-man-alog-_a2b-blog-_ab-2b-gia-tri-cua-log-_ab-bang.html/feed 0   Cho \(x,\,y\) là hai số thực dương khác \(1.\) Biết \({\log _3}x = {\log _y}9\) và \(xy = 81.\)  Khi đó \(\log _3^2\left( {\frac{x}{y}} \right)\) bằng https://booktoan.com/cho-xy-la-hai-so-thuc-duong-khac-1-biet-log-_3x-log-_y9-va-xy-81-khi-do-log-_32left-fracxy-right-bang.html https://booktoan.com/cho-xy-la-hai-so-thuc-duong-khac-1-biet-log-_3x-log-_y9-va-xy-81-khi-do-log-_32left-fracxy-right-bang.html#respond Mon, 13 May 2024 17:00:00 +0000 https://booktoan.com/cho-xy-la-hai-so-thuc-duong-khac-1-biet-log-_3x-log-_y9-va-xy-81-khi-do-log-_32left-fracxy-right-bang.html https://booktoan.com/cho-xy-la-hai-so-thuc-duong-khac-1-biet-log-_3x-log-_y9-va-xy-81-khi-do-log-_32left-fracxy-right-bang.html/feed 0