{"common":{"save":0,"post_id":"7110","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5464","post_id":"7110","mon_id":"1158924","chapter_id":"1159168","question":"<p>Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$\\log_2(2x+1)=4$<\/span> có nghi\u1ec7m là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x=\\dfrac{3}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x=\\dfrac{17}{2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x=\\dfrac{15}{2}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x=\\dfrac{13}{6}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$x=\\dfrac{15}{2}$<\/span><\/span><\/p><p>Ph\u01b0\u01a1ng trình \u0111ã cho t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi <\/p><p><span class=\"math-tex\">$\\log_2(2x+1)=\\log_216$<\/span> ⇔ 2x + 1 = 16 ⇔ <span class=\"math-tex\">$x=\\dfrac{15}{2}$<\/span>.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình \u0111ã cho có nghi\u1ec7m là <span class=\"math-tex\">$x=\\dfrac{15}{2}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 04:03:44","option_type":"math","len":0},{"id":"5466","post_id":"7110","mon_id":"1158924","chapter_id":"1159168","question":"<p>S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$\\log(x^2+4)=\\log4x$<\/span> là:<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> 2","<strong>C.<\/strong> 3","<strong>D.<\/strong> 1"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> 1<\/span><\/p><p>\u0110i\u1ec1u ki\u1ec7n xác \u0111\u1ecbnh: <span class=\"math-tex\">$\\begin{cases}x^2+4>0\\\\4x>0\\end{cases}$<\/span> ⇔ x > 0.<\/p><p>V\u1edbi \u0111i\u1ec1u ki\u1ec7n trên ta có: <span class=\"math-tex\">$\\log(x^2+4)=\\log4x$<\/span><\/p><p>⇔ <span class=\"math-tex\">$x^2+4=4x$<\/span> ⇔ <span class=\"math-tex\">$x^2-4x+4=0$<\/span> ⇔ x = 2 (th\u1ecfa \u0110KX\u0110).<\/p><p>V\u1eady ph\u01b0\u01a1ng trình có 1 nghi\u1ec7m.<\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2024-04-07 04:07:52","option_type":"txt","len":0},{"id":"5467","post_id":"7110","mon_id":"1158924","chapter_id":"1159168","question":"<p>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$2\\log_2x=\\log_2(2x+3)$<\/span> là:<\/p>","options":["<strong>A.<\/strong> S = {–1; 3}","<strong>B.<\/strong> S = {3}","<strong>C.<\/strong> S = {1; –3}","<strong>D.<\/strong> S = ∅"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> S = {3}<\/span><\/p><p>\u0110i\u1ec1u ki\u1ec7n <span class=\"math-tex\">$\\begin{cases}x>0\\\\2x+3>0\\end{cases}$<\/span> ⇔ x > 0.<\/p><p>Ta có: <span class=\"math-tex\">$2\\log_2x=\\log_2(2x+3)$<\/span> ⇔ <span class=\"math-tex\">$\\log_2x^2=\\log_2(2x+3)$<\/span> ⇔ <span class=\"math-tex\">$x^2-2x-3=0$<\/span><\/p><p>⇔ x = 3 ho\u1eb7c x = –1<\/p><p>\u0110\u1ed1i chi\u1ebfu v\u1edbi \u0111i\u1ec1u ki\u1ec7n ta lo\u1ea1i x = –1.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình có t\u1eadp nghi\u1ec7m S = {3}.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 04:16:36","option_type":"txt","len":2}]}
