{"common":{"save":0,"post_id":"7100","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5363","post_id":"7100","mon_id":"1158924","chapter_id":"1159168","question":"<p>Cho a, b, c l&agrave; c&aacute;c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m&atilde;n&nbsp;<span class=\"math-tex\">$\\log_5a=x$<\/span>,&nbsp;<span class=\"math-tex\">$\\log_5b=y$<\/span>,&nbsp;<span class=\"math-tex\">$\\log_5c=z$<\/span>. Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$E=\\log_\\sqrt{5}\\bigg(\\dfrac{a^3b^2}{\\sqrt{c}}\\bigg)$<\/span>&nbsp;l&agrave;<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}x+y-\\dfrac{1}{4}z$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$3x+2y-\\dfrac{1}{2}z$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$6x+4y-z$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}x+y+\\dfrac{1}{4}z$<\/span>"],"correct":"3","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$E=\\log_\\sqrt{5}\\bigg(\\dfrac{a^3b^2}{\\sqrt{c}}\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=2\\log_5\\bigg(\u200b\u200b\\dfrac{a^3b^2}{\\sqrt{c}}\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=2\\bigg(\\log_5a^3+\\log_5b^2-\\log_5c^\\frac{1}{2}\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=2\\bigg(3\\log_5a+2\\log_5b-\\dfrac{1}{2}\\log_5c\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=6\\log_5a+4\\log_5b-\\log_5c$<\/span><\/p><p><span class=\"math-tex\">$=6x+4y-z$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$6x+4y-z$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-10 05:30:09","option_type":"math","len":0},{"id":"5366","post_id":"7100","mon_id":"1158924","chapter_id":"1159168","question":"<p>Cho a, b l&agrave; c&aacute;c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m&atilde;n&nbsp;<span class=\"math-tex\">$\\log_2a=3,\\log_2b=7$<\/span>. Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$F=\\log_{ab}\\bigg(\\dfrac{a^2}{b}\\bigg)$<\/span>&nbsp;l&agrave;<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{1}{10}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{10}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{7}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{7}{3}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$F=\\log_{ab}\\bigg(\\dfrac{a^2}{b}\\bigg)$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{\\log_2\\bigg(\\dfrac{a^2}{b}\\bigg)}{\\log_2 ab}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{2\\log_2a-\\log_2b}{\\log_2a+\\log_2b}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{2.3-7}{3+7}$<\/span>&nbsp;<span class=\"math-tex\">$=-\\dfrac{1}{10}$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$-\\dfrac{1}{10}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 02:50:13","option_type":"math","len":0},{"id":"5367","post_id":"7100","mon_id":"1158924","chapter_id":"1159168","question":"<p>Cho a, b l&agrave; c&aacute;c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng th\u1ecfa m&atilde;n&nbsp;<span class=\"math-tex\">$\\log_ab=\\dfrac{b}{8},\\log_2a=\\dfrac{16}{b}$<\/span>&nbsp;. Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c G = a + b l&agrave;<\/p>","options":["<strong>A.<\/strong> 10","<strong>B.<\/strong> 20","<strong>C.<\/strong> 12","<strong>D.<\/strong> 24"],"correct":"2","level":"2","hint":"","answer":"<p>V&igrave;&nbsp;&nbsp;<span class=\"math-tex\">$\\log_ab=\\dfrac{b}{8},\\log_2a=\\dfrac{16}{b}$<\/span>&nbsp; n&ecirc;n&nbsp;&nbsp;<span class=\"math-tex\">$\\log_2a.\\log_ab=\\dfrac{16}{b}.\\dfrac{b}{8}$<\/span>&nbsp;<\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\log_2b=2$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$b=2^2=4$<\/span>.<\/p><p>Khi \u0111&oacute;&nbsp;<span class=\"math-tex\">$\\log_2a=\\dfrac{16}{b}=\\dfrac{16}{4}=4$<\/span>&nbsp;&rArr;&nbsp;<span class=\"math-tex\">$a=2^4=16$<\/span><\/p><p>Do \u0111&oacute; G = a + b = 16 + 4 = 20.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong> 20.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 02:55:26","option_type":"txt","len":0}]}