{"common":{"save":0,"post_id":"7101","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5385","post_id":"7101","mon_id":"1158924","chapter_id":"1159168","question":"<p>\u0110\u1eb7t&nbsp;<span class=\"math-tex\">$a=\\ln2$<\/span>,&nbsp;<span class=\"math-tex\">$b=\\ln3$<\/span>. H&atilde;y bi\u1ec3u di\u1ec5n&nbsp;<span class=\"math-tex\">$\\ln36$<\/span>&nbsp;theo a v&agrave; b.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$2a+2b$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$a+b$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$a-b$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$2a-2b$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p><span class=\"math-tex\">$\\ln36=\\ln(2^2.3^2)$<\/span>&nbsp;<span class=\"math-tex\">$=2\\ln2+2\\ln3$<\/span>&nbsp;<span class=\"math-tex\">$=2a+2b$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$2a+2b$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 03:53:35","option_type":"math","len":0},{"id":"5388","post_id":"7101","mon_id":"1158924","chapter_id":"1159168","question":"<p>Cho x, y, z l&agrave; c&aacute;c s\u1ed1 th\u1ef1c d\u01b0\u01a1ng t&ugrave;y &yacute; kh&aacute;c 1 v&agrave; xyz&nbsp;<span class=\"math-tex\">$\\ne$<\/span>&nbsp;1. \u0110\u1eb7t&nbsp;<span class=\"math-tex\">$a=\\log_xy$<\/span>,&nbsp;<span class=\"math-tex\">$b=\\log_zy$<\/span>. T&iacute;nh&nbsp;<span class=\"math-tex\">$\\log_{xyz}(y^5z^3)$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{5ab+3a}{a+b+1}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{5ab+3b}{ab+a+b}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{5ab+3a}{ab+a+b}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{5ab+3b}{a+b+1}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p><span class=\"math-tex\">$\\log_{xyz}(y^5z^3)$<\/span><span class=\"math-tex\">$=5\\log_{xyz}y+3\\log_{xyz}z$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{5}{\\log_y(xyz)}+\\dfrac{3}{\\log_z(xyz)}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{5}{\\log_yx+\\log_yz+1}+\\dfrac{3}{\\log_zx+\\log_zy+1}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{5}{\\log_yx+\\log_yz+1}+\\dfrac{3}{\\log_zy.\\log_yx+\\log_zy+1}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{5}{\\dfrac{1}{a}+\\dfrac{1}{b}+1}+\\dfrac{3}{\\dfrac{b}{a}+b+1}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{5ab}{ab+a+b}+\\dfrac{3a}{ab+a+b}$<\/span><\/p><p><span class=\"math-tex\">$=\\dfrac{5ab+3a}{ab+a+b}$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{5ab+3a}{ab+a+b}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 04:06:28","option_type":"math","len":0},{"id":"5390","post_id":"7101","mon_id":"1158924","chapter_id":"1159168","question":"<p>Cho a, y, z l&agrave; c&aacute;c s\u1ed1 th\u1ef1c l\u1edbn h\u01a1n 1 v&agrave; g\u1ecdi w l&agrave; s\u1ed1 th\u1ef1c d\u01b0\u01a1ng sao cho&nbsp;<span class=\"math-tex\">$\\log_xw=12$<\/span>,&nbsp;<span class=\"math-tex\">$\\log_yw=20$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$\\log_{xyz}w=6$<\/span>. T&iacute;nh&nbsp;<span class=\"math-tex\">$\\log_zw$<\/span>.<\/p>","options":["<strong>A.<\/strong> 34","<strong>B.<\/strong> &ndash;30","<strong>C.<\/strong> 30","<strong>D.<\/strong> &ndash;34"],"correct":"3","level":"3","hint":"","answer":"<p><span class=\"math-tex\">$\\log_{xyz}w=6$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$\\log_w(xyz)=\\dfrac{1}{6}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\log_wx+\\log_wy+\\log_wz=\\dfrac{1}{6}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\dfrac{1}{12}+\\dfrac{1}{20}+\\log_wz=\\dfrac{1}{6}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\log_wz=\\dfrac{1}{30}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\log_zw=30$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong> 30.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 04:13:35","option_type":"txt","len":1}]}