Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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HomeLớp 11Toán lớp 11 - Sách kết nối tri thứcBài 21. Phương trình, bất phương trình mũ và lôgaritBài tập trung bình
{"common":{"save":0,"post_id":"7106","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5420","post_id":"7106","mon_id":"1158924","chapter_id":"1159168","question":"<p>Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$9^x-6^x=2^{2x+1}$<\/span> có bao nhiêu nghi\u1ec7m?<\/p>","options":["<strong>A.<\/strong> 3","<strong>B.<\/strong> 2","<strong>C.<\/strong> 1","<strong>D.<\/strong> 0"],"correct":"3","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$9^x-6^x=2^{2x+1}$<\/span><\/p><p>⇔ <span class=\"math-tex\">$9^x-6^x-2.4^x=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$\\bigg(\\dfrac{9}{4}\\bigg)^x-\\bigg(\\dfrac{3}{2}\\bigg)^x-2=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$\\bigg(\\dfrac{3}{2}\\bigg)^{2x}-\\bigg(\\dfrac{3}{2}\\bigg)^x-2=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$\\bigg(\\dfrac{3}{2}\\bigg)^x=-1$<\/span> (vô nghi\u1ec7m) ho\u1eb7c <span class=\"math-tex\">$\\bigg(\\dfrac{3}{2}\\bigg)^x=2$<\/span><\/p><p>⇔ <span class=\"math-tex\">$\\bigg(\\dfrac{3}{2}\\bigg)^x=2$<\/span> <\/p><p>⇔ <span class=\"math-tex\">$x=\\log_\\frac{3}{2}2$<\/span>.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình có m\u1ed9t nghi\u1ec7m.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 1.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-04 01:40:08","option_type":"txt","len":0},{"id":"5423","post_id":"7106","mon_id":"1158924","chapter_id":"1159168","question":"<p>Áp su\u1ea5t không khí P (\u0111o b\u1eb1ng milimet thu\u1ef7 ngân, kí hi\u1ec7u là mmHg) suy gi\u1ea3m m\u0169 so v\u1edbi \u0111\u1ed9 cao x (\u0111o b\u1eb1ng mét), t\u1ee9c là P gi\u1ea3m theo công th\u1ee9c <span class=\"math-tex\">$P=P_0.e^{xi}$<\/span> , trong \u0111ó <span class=\"math-tex\">$P_0=760$<\/span> mmHg là áp su\u1ea5t \u1edf m\u1ef1c n\u01b0\u1edbc bi\u1ec3n (x = 0), i là h\u1ec7 s\u1ed1 suy gi\u1ea3m. Bi\u1ebft \u1edf \u0111\u1ed9 cao 1000 m thì áp su\u1ea5t không khí là<br \/>672,71 mmHg. H\u1ecfi áp su\u1ea5t không khí \u1edf \u0111\u1ed9 cao 3000 m g\u1ea7n v\u1edbi s\u1ed1 nào sau \u0111ây nh\u1ea5t?<\/p>","options":["<strong>A.<\/strong> 536,8 mmHg","<strong>B.<\/strong> 546,8 mmHg","<strong>C.<\/strong> 526,8 mmHg","<strong>D.<\/strong> 516,8 mmHg"],"correct":"3","level":"2","hint":"","answer":"<p>\u1ede \u0111\u1ed9 cao 1000 m, ta có <span class=\"math-tex\">$672,71=760.e^{1000i}$<\/span> ⇔ <span class=\"math-tex\">$e^{1000i} \\approx 0,885$<\/span> .<\/p><p>\u1ede \u0111\u1ed9 cao 3000 m, ta có <span class=\"math-tex\">$P=760.e^{3000i}=760.(e^{1000i})^3$<\/span> <span class=\"math-tex\">$\\approx 760.0,885^3 \\approx 526,8$<\/span> mmHg.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 526,8 mmHg.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-04 01:52:37","option_type":"txt","len":1},{"id":"5425","post_id":"7106","mon_id":"1158924","chapter_id":"1159168","question":"<p>S\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$\\log_3(x^2+4x)+\\log_\\frac{1}{3}(2x+3)=0$<\/span> là<\/p>","options":["<strong>A.<\/strong> 1","<strong>B.<\/strong> 2","<strong>C.<\/strong> 0","<strong>D.<\/strong> 3"],"correct":"1","level":"2","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n <span class=\"math-tex\">$\\begin{cases}x^2+4x>0\\\\2x+3>0\\end{cases}$<\/span> ⇔ <span class=\"math-tex\">$\\begin{cases}x>0\\text{ ho\u1eb7c }x <-4\\\\x>-\\dfrac{3}{2}\\end{cases}$<\/span> ⇔ <span class=\"math-tex\">$x>0$<\/span>.<\/p><p>Ph\u01b0\u01a1ng trình \u0111ã cho ⇔ <span class=\"math-tex\">$\\log_3(x^2+4x)=\\log_3(2x+3)$<\/span><\/p><p>⇔ <span class=\"math-tex\">$x^2+4x=2x+3$<\/span> ⇔ <span class=\"math-tex\">$x^2+2x-3=0$<\/span> ⇔ <span class=\"math-tex\">$x=1$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=-3$<\/span>.<\/p><p>K\u1ebft h\u1ee3p v\u1edbi \u0111i\u1ec1u ki\u1ec7n ta \u0111\u01b0\u1ee3c x = 1.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình có m\u1ed9t nghi\u1ec7m.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 1.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-04 02:00:53","option_type":"txt","len":0}]}