{"common":{"save":0,"post_id":"7105","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5402","post_id":"7105","mon_id":"1158924","chapter_id":"1159168","question":"<p>Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$4^{2x-3}=5$<\/span> là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}+\\log_45$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}+\\log_25$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}+\\dfrac{1}{4}\\log_25$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$3+\\log_45$<\/span>"],"correct":"3","level":"1","hint":"","answer":"<p>Ta có <span class=\"math-tex\">$4^{2x-3}=5$<\/span> ⇔ <span class=\"math-tex\">$2x-3=\\log_45$<\/span> ⇔ <span class=\"math-tex\">$2x=3+\\dfrac{1}{2}\\log_25$<\/span> ⇔ <span class=\"math-tex\">$x=\\dfrac{3}{2}+\\dfrac{1}{4}\\log_25$<\/span> .<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}+\\dfrac{1}{4}\\log_25$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-03 01:34:51","option_type":"math","len":0},{"id":"5404","post_id":"7105","mon_id":"1158924","chapter_id":"1159168","question":"<p>Tìm t\u1ea5t c\u1ea3 các giá tr\u1ecb th\u1ef1c c\u1ee7a m \u0111\u1ec3 ph\u01b0\u01a1ng trình <span class=\"math-tex\">$7^{2x-1}+2m^2-m=3$<\/span> có nghi\u1ec7m.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$m\\in \\bigg(-1;\\dfrac{3}{2}\\bigg)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$m\\in \\bigg(\\dfrac{1}{2};+\\infty\\bigg)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$m\\in (0;+\\infty)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$m\\in \\bigg[-1;\\dfrac{3}{2}\\bigg]$<\/span>"],"correct":"1","level":"1","hint":"","answer":"<p><span class=\"math-tex\">$7^{2x-1}+2m^2-m=3$<\/span> ⇔ <span class=\"math-tex\">$7^{2x-1}=-2m^2+m+3$<\/span><\/p><p>Ph\u01b0\u01a1ng trình \u0111ã cho có nghi\u1ec7m khi <span class=\"math-tex\">$-2m^2+m+3>0$<\/span> ⇔ <span class=\"math-tex\">$-1< m < \u200b\\dfrac{3}{2}\u200b$<\/span> .<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$m\\in \\bigg(-1;\\dfrac{3}{2}\\bigg)$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-03 01:42:09","option_type":"math","len":0},{"id":"5406","post_id":"7105","mon_id":"1158924","chapter_id":"1159168","question":"<p>Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$16^{x-2}=0,25.2^{-x+4}$<\/span> là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x=-2$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x=1$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x=\\dfrac{1}{5}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x=2$<\/span>"],"correct":"4","level":"1","hint":"","answer":"<p><span class=\"math-tex\">$16^{x-2}=0,25.2^{-x+4}$<\/span><\/p><p>⇔ <span class=\"math-tex\">$2^{4(x-2)}=2^{-2}.2^{-x+4}$<\/span><\/p><p>⇔ <span class=\"math-tex\">$2^{4x-8}=2^{-x+2}$<\/span><\/p><p>⇔ <span class=\"math-tex\">$4x-8=-x+2$<\/span><\/p><p>⇔ <span class=\"math-tex\">$x=2$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$x=2$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-03 01:46:37","option_type":"math","len":0}]}
