{"common":{"save":0,"post_id":"7104","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5447","post_id":"7104","mon_id":"1158924","chapter_id":"1159168","question":"<p>Cho các hàm s\u1ed1 <span class=\"math-tex\">$y=a^x$<\/span> và <span class=\"math-tex\">$y=b^x$<\/span> v\u1edbi a, b là nh\u1eefng s\u1ed1 th\u1ef1c d\u01b0\u01a1ng khác 1 có \u0111\u1ed3 th\u1ecb nh\u01b0 hình v\u1ebd. \u0110\u01b0\u1eddng th\u1eb3ng y = 3 c\u1eaft tr\u1ee5c tung, \u0111\u1ed3 th\u1ecb hàm s\u1ed1 <span class=\"math-tex\">$y=a^x$<\/span> và <span class=\"math-tex\">$y=b^x$<\/span> l\u1ea7n l\u01b0\u1ee3t t\u1ea1i H, M, N, bi\u1ebft HM = 2MN. M\u1ec7nh \u0111\u1ec1 nào sau \u0111ây là <strong>\u0111úng<\/strong>?<\/p><p><span class=\"svgedit\"><svg height=\"278\" width=\"230\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"280\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"278\" id=\"svg_1\" width=\"230\" x=\"0\" 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K6SilShkxd+60gWSQlYU0fGaZ0Xff2SBJBRTTQcKbomvXTvJoLHLEQkreW6YciukgY8aY1jKpBbSUklDVqqYbO2qUDZJUQTEd5JJLlB57+eILG0gGKAwEKY85RktKUgvFdBDcX2LBzR9\/2EAyuPpqMxLLfD5OQDEd4\/XXTTe2ffsktlorVpjW8oQTkvxpQPKDYjpGly5GzB9\/TJKY2QoEKVTwIk5AMR2jRg3Uv0xia\/nrr6JKlxY591wbIC5AMR0ivEQV6VuTRQgZpNFaYuMncQaK6RDnnGNyxyZrmkTNnaul1NMkHIl1CorpCGgt09PN\/WXS9l5iJBY\/cMIEGyCuQDEdYe5cpRfd3HijDSSaL74QhS5serrIvn02SFyBYjpCeFN00rqxl15qfuCCBTZCXIJiOkLJkuFpEhtIJDt2iELz3KKFDRDXoJgxEgqFDh7qMAMm2Z9bEOvWmcYrWbljQ5UqmR+IZXjESShmjGzYsEE+\/PBDOfbYY+XKK6+00bysXbtWatSoId27d5f169fLfqQkyAdcMjzBApyEg5FYfAK0a2cDxEVSKuauXbtkxowZ+k1++umny\/Tp0\/UbHy3RAu\/ep0+fPlK3bl0ZNWqULD5MBeNkdmUHDhwoTz31lNSsWdNGcgIRZ8+e7XVPS8rvv\/9uo\/lz6qlKKlbE72ADCUQhRyw+BbzrC\/PVV1\/JRx99JFWqVJHWrVvbqCErK8u77x0jJ598stx\/\/\/2yatUq+whJJClvMTMzM733SZrsjpBx6rHHHpMTTjhB\/owi2XAyxbztttvktddek+OPP16\/cXPz5ptv6gPXfjj27jWeXHKJDSQQ9d575oeddVaeeUt8KOIo4bWm+FDMTePGje1XJBmkXMwRI0ZI+fLlZV+EIXu0SFdjri0KkiUmuqRTvXuzmTNnSiXvXm379u32EcM01DTwQOvz8ssv668LonNnM+gzYEASJvgvuECkXLmIafdef\/11OXDggO653H777TZq+Oabb7z7YO9GmCSNlIvZq1cvr7XI21z88ccfuiXdunWrjRRMssTEB8isWbP0dZUpU0bWYNe\/Za\/X\/I0dO1Y\/p0KFCvLBBx\/YRyKD287jjsMtXxKktPst5fLLbSAnuF0A6Lai1cTfPwx+30gfnCRxpFzMhg0bSseOHe3ZIfr27atb0mhJlpjDhg2TX2zxVnxwLFu2TH+N++JHHnlEf\/3ZZ5\/pxyBqQYRTiHifTYkF14HV8fhh+dwW9O7d235lWvvs95r\/+c9\/DjsCTeJLysXEG3jRokWyfPnyHEezZs3k2hhWcydLzGrVqtmvsIQuXebMmaO\/xjWHR14\/\/fRT\/XsdjueeM66MHJngN\/0bb+gfpAYNsoGcTJ48WV9\/GNzbH3nkkfKzTfZ8KRYjkKSSUjHfeecdKYtqUrnAGxz3lxgFjJZkiLlt2zbvPe69yS033XSTvh+bP3++\/nAJg2kS\/G4FgTEjdGEh5q5dNpgINm0yS+8wRYKa8RHIfR+PkWR8sKB7i\/vLSINBJLGkVMxatWrJNddcY88OgZFaTDVgGD9akiHm+PHjc4wQ4\/yUU06RKdk2GGOUFm\/qw02TeN+qpUz4aOwdd5jWEmv+IoDf59VXX7Vnhxg8eLC+18Tfk93Y5JMyMffs2aO7hRiVzQ3eKKVKlbJn0ZFIMfHGXLFihXTt2lV\/WIQHRjZu3Cj16tXTj0PILVu26G7gUUcdpRcYFDRg8ve\/m3l+r0FLHD\/8YKSsXdvcZ0YA14gWPzcYhcUAVocOHWyEJJOUiIkWEfdmaFkwihl+o6ML+9tvv0lGRob06NEjppHARIq5efNmGT16tJ4mQVcWAgJcX3j+defOnXrKAa3ohAkTdDcQckYCDVD58kowzen9uokBLXuDBsb+CClD8GGCa8d8LBZ5YKokNxiYGz58uD0jySQNn\/TJPh566CF58skn9X\/6E088oVtIxN9++23d4iA+dOhQefTRR\/N8b34Huo4Q884774z4uEvH1Kno7mZJ69b7Iz4el2PlSsnypDxw3XURH1+9erUe+cbfGn\/zcePG5XkOPuzQQ8gd55H4w2u00nTLxYMHD4cOdCt9fWzdKplelyvT+2UOHmXKyN4hQyI\/PxWH15pndu+e8xpxdOokmb\/+Gvl7Yjz29u+f5\/X3lisnmdu2RXw+D7ePlI7KxgN1\/fV6gCPi8e239lkpJrySINIxaZJ9UhHAwvJIr+0d6sEH7ZOIn\/D+93wO1rRFeEPi6NPE6xLcmvpjXvXI14fjx\/KRvyeWY1j9yK+tj3r17B+K+Anvf87nIB9qpDekd7zatalc\/crVKT8Wtjg94vXh2HRarYjfE8vx8RUNI762PpKxbYXEHe9\/zt+Ebrst75vRO0Kow5GVd0tWSti7VxRWOOW+TszVxmMi0\/s9Q0janPv1vUMNHWqfRPyE97\/nf9TTT+d4M4ZOPFHELjR3hqVL5fe0jIPXqEWNZwGf55\/P8TeA9Oqtt+yDxG94\/4PB4I\/du+XCjAwZnGsvoSsMHaqkdFqW3Nhkjcjq1fFNHuu9nipTRgSyf\/klVtSzOJDPCYyYyVgrW1iQi6t5c7NoPcIe5SKjsEULrfAnn9gI8TsUMwlkZprGrFUrG4gnqG6LrmubNjZAggDFTALdupntXf37x3mXBu6jkSoEA135bOki\/oRiJhisw8c6cogZ75okBxdXvPSSjZCgQDETzIcfGnds1pG4oUaO1C+sN0AfJoUJ8R8UM8E0b670dOWSJTYQL+rXF8HcJbuwgYRiJpCVK01rWbGiyi8HVuxgM+ett5oXRnYCEkgoZgK57joz6LNwYRwHfT7\/3Ny0nnSSDZAgQjETSIUKKr7+IAsfTMe95fvv2yAJIhQzQTz\/vGktMXAaNx54wIg5ZIgNkKBCMRMA7iczMoyYv\/5qg0VEYd8murB16rACdDGAYiaAmTONlD16xOneEolna9QQhVHYeC58J85CMRNAo0amxzlzpg0UBSy0Re5dvOAzz9ggCToUM84gRzUcysgwMxtFRSdq9l4wxEwExQqKGWfC+7Z37rSBouD9TvrFKlRAiWobJMUBihlH0OvEtshzzsm3qFb04AWaNNFiqo8\/tkFSXKCYcQTVBNHAPf540fuwqmdPI2WUhXtJsKCYcQL1dY880pQ+KDIo7QfDjznGvRQpJClQzDhhN3tIhBpJsbFunaj0dJOoa+lSGyTFDYoZB7DrClJi\/n\/PHhssJApFYtGFHTDARkhxhGLGgQEDzIKCfAo2R01YSn2zSoo1FDMOHH20kooVRbZvt4HCgF0jJUuKwtRIwmrzEb9AMYtIv34h3ci1b1+EQR+sSsA8C15o2TIbJMUZilkEcG9Zs6YZicWOrELTuLGRMp9y7KT4QTGLwPjxxqf777eBWDlwQBRqi+BFbrnFBgmhmIUGO6\/gE0ZiN260wVh55x39Iqp2bRsgxEAxC8nLLxsx+\/Yt5L3lu+\/qFwjBbGSEJiQbFLOQHHWUeD+vkMW6MOpaubJJz85FBCQCFLMQ9O5t5i27di1Eaxne9IwuLBenk3ygmDGCIlqeV1K1qg3EAlpKVBeClH362CAheaGYMXLHHaa17N\/fBmJA9eqlpQxdfLGNEBIZihkDK1Zor\/S9ZUzZCbwnq3CS5lNPZTItclgoZgzcdJNpLSdPtoEoURMmmHmVE06If2UhEkgoZpRgiyTcwlLWWIo1qxkzTEuJY\/16GyWkYChmlDRpYlrLVatsIBomTRJVvrwp\/sM1sCQGKGYUjB1rpGzXLoYbS1ThOvZYXVhWffCBDRISHRTzMCCTOho9FG1G+pCowP4vVHr2bFbPPmuDhEQPxTwMb7xhWsuRI6NsLZHCAN+A4403bJCQ2KCYBYDcsGHHol3OqpBAC98wbFiMcyqEHIJiFsBllxnHZs+OQrDdu02VZ+8bdIoQJJklpJBQzHwYPtx0YZs2VYd3DFK2bGmkvOEGGySk8FDMCGDsplIlk0Hy559tMD8wqdmqlZGyWzcbJKRoUMwIPPCAaS2x57JA9u0ThWI\/ePLf\/sZ7ShI3KGYusBMLnmGKpEC8nxeyUyJy5502SEh8oJi5qF5deV1YJd98YwP5cHD0Fdu3srJslJD4QDGzgfo9cO2661T+vVLvnlJhMTqeiCxcXJROEgDFtCxfbhbrnHWWDUTiq69EeT8DUqq+fW2QkPhDMT2w1K5sWTPgM21a5KZSzZtnsqQjW\/rzz9soIYmBYnpg7AZSPvKIDeTmyy9FYbFserqoV16xQUISR7EXM7yQ4KSTIo\/h6IRZeAJKGGBvJSFJoFiL6X2LLgZUsqTSyevygCYUUuJYs8YGCUk8xVbMP\/8UqVXLFAQaPtwGw3hNp8KCATzYoEEUy38IiS\/FVsxwtrsuXWwgzIYNh1avt2\/P6RCSEoqlmBMnGimPOELJjh026KFQoxJzlCVKiLrqKu4QISmj2IkJEdPTlffcbFkkkV5y5kwzwOMd6u9\/tw8QkhqKlZi4r0xPN\/eVgwfb+UpIOWCA6bpiSmTiRBMnJIUUKzFbtDBd2MGDbQDzI7Zkga55sHmzfYCQ1FJsxEROLPhXrZqS33\/3GsoFC3Cig6pz59iSxRKSYIqFmKNGmZaydm1bkn34cFHI3ozldU8+aZ5EiEMEXkzkWU5PF8nIEFkyaZuoCy80TWfNmiLr1tlnEeIWgRZzyxbTUuL44B+LzRfeoRo2tM8gxE0CLWa1ahiBVfJ9JU9ECAkxWcGZ+IBAirl3r9lXWT9tlaxLq22kRLXZH36wzybEbQInZq9ed0ubi7PkmbSHZH9aGS2lYP8kbCXEJwROzHNKXCBfpjU2QjZoIGrcOPsMQvxDcMTct0+OqJAud0PI0qUl1KkTF6AT3xIMMb\/8UjI9GY\/wpLwLmZo3bbIPEOJPfC9mqHVrvRvkf56UEDPSAgNC\/IZ\/xcTuZiTH8mT8Kq2BNK20TNLTI6\/8IcRv+E\/M+fNFzjxTC4nj3rShcn6zkGRm5p3HJMSv+EfMNWtE3XKLljGUVkKeT7tPSqdlSYcOZpNIpAUGhPgV98XEVpChQ00L6d1Lbq13kTQvs0iftmt3KMMAxSRBwl0xPdF0qXTbZVVHHy0rR87TWe2wMaRbt5xpPygmCRJuirl588FSBPqYOVNeH7kf05P6NE9WOw+KSYKEU2Kql18Wddpph4R89FGRPXvk9ttRgcsMwn76aeQSBhSTBAk3xHz7bZH69Q8JidwfmzbpJMxXXWW2bp1xhsiiRfb5EaCYJEikTsz9+0WNHi0KxoWF7NpV5Mcf9cOYFUGuZYQvv1xk504dzheKSYJE8sX87TdRY8eKwigOrMO95A03HCwcgkx2U6cqnUmybFkM8qio0rtSTBIkkiemJ6SMHCn6ZhFCejeMCgvNYaIFMyPh4rHwdcqU\/KrH5oVikiCReDE98RTWs9rlc\/oYMsRYmA1sl8zIMPeTlSqFZPdu+0CUUEwSJBIn5owZopo1OyTjcceJzJqVZ8MySqp37ap0ruWws4WBYpIgEV8x9+wRdd99KKN1UEh10UUiqDEZAXganh2pXl3J11\/bBwoBxSRBouhi4h7RE0\/17HlIRtw\/okxzPukhUVq9Tx+zgqd0aSUDB0Y3wFMQFJMEicKLiUKuGF0N90E9y5AWMvT00\/YJeUFCgTlzTKFYfEujRiKLF9sHiwjFJEEiNjExYPPttxLCPIZtHZFNOdSyZY7R1UhgerJECVPQp1w5kUGDoh9xjQaKSYJEdGLOmyehunWNUVbIENJBfvONSGamfVJkMD2JYj7hWRIM9Hi3onGHYpIgkb+YU6aIatfu0EIAHMinM3581FWxunSBkKbbiqJaqAuLUdhEQDFJkMgp5qpVIjffrAdvwjKqevVEUHjn++\/tkwrml19EHnxQ5MgjjZBHHRWSMWMSJ2QYikmCRE4xsTIHNjVuLApv8Bgyl\/\/8s+jR1XALiWmQ556zDyYBikmCRE4xC8H69SL9+5tizBDyhBNE\/vnPBDePEaCYJEgUSkzMOaLL2qCBGWXFfCR6v6mskk4xSZCIWcwPPlBy4ommdcRRu7bI2rUHN4ekDIpJgkRUYmIO8oorVLgyutdCKvnb35QeZXUFikmCRL5iYpdWv35KmjY91DpWrqzk6aeVXlLnGhSTBIkcYu7bZ7J8tGplRlZxYJT12muVnr50GYpJgkQOMZ944pCQSOsxbFjyR1cLC8UkQSKHmAC5dRK9GCARUEwSJPKI6VcoJgkSFJMQB6GYhDgIxSTEQSgmIQ5CMQlxEIpJiINQTEIchGIS4iAUkxAHoZiEFIJ169bJ1q1bJVTUTOX5QDEJKQRpaWlSsmRJqVChgpxyyimybNky+0h8yCHmvHnz5LzzzvPl0ahRIylVqpRUr1494uM8eMTzgJi5D4h6zDHHSOPGjeXWW2+VH20R5sKQQ8wxY8ZE\/IE8ePCI7WjRooUMGTJEJkyYUKjuLruyhBSC7BJWq1ZNunXrJv369ZOFCxfG5b6TYhJSCNq1aycvvPCC\/IYcPAnAF2IeOHBAdu3aJXtQfzOfXdwUkwQJp8WEbK1bt5Znn31W9u3bJ2vXrpXjjjtO\/vvf\/9pnHIJikiDhrJj9+\/eX6667Tn5G7YVsZGVlScuWLeW1116zEQPFJEHCSTEffvhhadasmWTmU+IP8mF65M9sNTkpJkkFaCjCt1f4F7dd8cA5MefPn6\/nIwuasL3nnnv0c7KLSzFJMoGQTzzxhCxYsEBuvPFGWbFihbz++usyceJEadu2rX1W4XFOTKyiqIQ6nAUA+TCZSzFJqsD7DHICNCKVK1fWXyN+6aWX6q+LglNi7t+\/X88LTZs2zUYi0717d6ldu3aObgPFJMlkJ\/K8Wjp37iwzZ860Z\/HBKTEHDRqkxYRkBVGuXDlp3769PTNQTJIqSpQoIcuXL7dn8cEpMTEtAjELokePHlpMzGlmh2KSVLBkyRKpWrWqnmcH69evlx07duivi4JTYu7du1eLmb2bkJ3vvvtO0tPTZe7cuTZyCIpJksXUqVOlbNmysnHjRhkxYoTUrFnTPoKq6gPznU2IBafEBD179pT69evr+83sLFq0SC8u+Dyf2n8UkySLlStX6nl2jMhOmTJFfz19+nQ9KhvY6RJw8803S+\/evWXx4sX6wJpExAqCYpIg4aSYhYFikiBBMQlxEIpJiINQTEIchGIS4iAUkxAHoZiEOEhgxEQCJGQmmzVrlo0Q4l8CIyYhQYJiEuIgFJMQB6GYhDgIxSTEQSgmIQ5CMQlxEIpJiINQTEIchGIS4iAUkxAHoZiEOAjFJMQ5RP4f0UkcYEWrOfgAAAAASUVORK5CYII=\" y=\"1\"><\/image> <\/g> <\/svg><\/span><\/p>","options":["<strong>A.<\/strong> 3a = 2b","<strong>B.<\/strong> 2a = b","<strong>C.<\/strong> a³ = b²","<strong>D.<\/strong> a² = b³"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> a² = b³<\/span><\/p><p>G\u1ecdi <span class=\"math-tex\">$M(x_1;3), N(x_2;3)$<\/span> v\u1edbi <span class=\"math-tex\">$x_1>0, x_2 > 0$<\/span>.<\/p><p>Theo gi\u1ea3 thi\u1ebft HM = 2MN ⇔ <span class=\"math-tex\">$HN=\\dfrac{3}{2}HM$<\/span> ⇒ <span class=\"math-tex\">$x_2=\\dfrac{3}{2}x_1$<\/span> (1).<\/p><p>Do <span class=\"math-tex\">$M(x_1;3)$<\/span> thu\u1ed9c \u0111\u1ed3 th\u1ecb hàm s\u1ed1 <span class=\"math-tex\">$y=a^x$<\/span>, <span class=\"math-tex\">$ N(x_2;3)$<\/span> thu\u1ed9c \u0111\u1ed3 th\u1ecb hàm s\u1ed1 <span class=\"math-tex\">$y=b^x$<\/span> nên<\/p><p><span class=\"math-tex\">$\\begin{cases}a^{x_1}=3\\\\b^{x_2}=3\\end{cases} $<\/span> ⇒ <span class=\"math-tex\">$a^{x_1}=b^{x_2}$<\/span> (2).<\/p><p>T\u1eeb (1) và (2) ta có <span class=\"math-tex\">$a^{x_1}=b^{\\frac{3}{2}x_1}$<\/span> ⇔ <span class=\"math-tex\">$a^{2x_1}=b^{3x_1}$<\/span> ⇔ <span class=\"math-tex\">$(a^2)^{x_1}=(b^3)^{x_1}$<\/span> ⇒ <span class=\"math-tex\">$a^2=b^3$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 02:17:54","option_type":"txt","len":2},{"id":"5449","post_id":"7104","mon_id":"1158924","chapter_id":"1159168","question":"<p>Tìm t\u1eadp xác \u0111\u1ecbnh c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=(x^2-1)^{-3}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$(-\\infty;-1)\\cup(1;+\\infty)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$(1;+\\infty)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$R\\setminus \\{\\pm 1\\}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$(-\\infty;-1)$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$R\\setminus \\{\\pm 1\\}$<\/span><\/span><\/p><p>Ta có hàm s\u1ed1 xác \u0111\u1ecbnh khi <span class=\"math-tex\">$x^2-1\\ne 0 \\Leftrightarrow x \\ne \\pm1$<\/span>.<\/p><p>V\u1eady <span class=\"math-tex\">$D=R\\setminus \\{\\pm1\\}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 02:23:16","option_type":"math","len":0},{"id":"5450","post_id":"7104","mon_id":"1158924","chapter_id":"1159168","question":"<p>T\u1eadp xác \u0111\u1ecbnh c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=(x+2)^{^\\dfrac{2}{5}}$<\/span> là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$[-2;+\\infty )$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$(-2;+\\infty )$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$(0;+\\infty )$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$R\\setminus\\{2\\}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$(-2;+\\infty )$<\/span><\/span><\/p><p>Vì <span class=\"math-tex\">$a=\\dfrac{2}{5}\\not\\in Z$<\/span> nên hàm s\u1ed1 xác \u0111\u1ecbnh x + 2 > 0 ⇔ x > –2.<\/p><p>V\u1eady <span class=\"math-tex\">$D=(-2;+\\infty)$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 02:29:34","option_type":"math","len":0}]}