{"paper":{"id":"site-2643","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":14,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2643/zad/3125","paper_id":"site-2643","number":"3125","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log36 jest równa A. 2log18 B. log40-2log2 C. 2log4-3log2 D. 2log6-log1","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-3125.svg","solution_image":"img/site/2643/rozw-3125.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/3126","paper_id":"site-2643","number":"3126","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log12 jest równa A. log3 * log4 B. log3 * log4 C. log16 - log4 D. log10 + log2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-3126.svg","solution_image":"img/site/2643/rozw-3126.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/3127","paper_id":"site-2643","number":"3127","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log24 jest równa A. 2log2+log20 B. log6+2log2 C. 2log6-log12 D. log30-log6","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-3127.svg","solution_image":"img/site/2643/rozw-3127.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/3283","paper_id":"site-2643","number":"3283","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log_3 1/27 jest równa A. -3, B. -1/3, C. 1/3, D. 3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-3283.svg","solution_image":"img/site/2643/rozw-3283.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/4358","paper_id":"site-2643","number":"4358","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wskaż liczbę, która spełnia równanie 4^x = 9. A. log 9 - log 4, B. log 2 / log 3, C. 2 * log_9 2, D. 2 * log_4 3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-4358.svg","solution_image":"img/site/2643/rozw-4358.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/5303","paper_id":"site-2643","number":"5303","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log_5 √125 jest równa A.2/3; B. 2; C. 3; D.3/2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-5303.svg","solution_image":"img/site/2643/rozw-5303.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/5465","paper_id":"site-2643","number":"5465","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Liczba 2log_5 4 - 3log_5 1/2 jest równa A. -log_5 7/2 B. 7log_5 2 C. -log_5 2 D. log_5 2","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-5465.svg","solution_image":"img/site/2643/rozw-5465.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/5763","paper_id":"site-2643","number":"5763","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Liczba 2\\log5 + 3\\log2 jest równa A. log(2⋅5) + log(3⋅2) B. log 2^5 + log 3² C. 2⋅3log(5⋅2) D. log(5^2⋅2^3)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-5763.svg","solution_image":"img/site/2643/rozw-5763.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/6645","paper_id":"site-2643","number":"6645","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wartość wyrażenia log_7 98 - log_7 2 jest równa A. 7 B. 2 C. 1 D. (-1)","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-6645.svg","solution_image":"img/site/2643/rozw-6645.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/6702","paper_id":"site-2643","number":"6702","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Na wykresie przedstawiono zależność log K(t), gdzie K(t) jest liczbą bakterii w próbce po czasie t wyrażonym w godzinach, jaki upłynął od chwili t=0 rozpoczęcia obserwacji. [rysunek] Gdy upłynęły dokładnie trzy godziny od chwili t=0, liczba K bakterii była równa A. 3 B. 100 C. 1000 D. 10000.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-6702.svg","solution_image":"img/site/2643/rozw-6702.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/6703","paper_id":"site-2643","number":"6703","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log_2[(√2)^2⋅(√2)^4⋅(√2)^8] jest równa A. √2 B. 7 C. 14 D. 2^7","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-6703.svg","solution_image":"img/site/2643/rozw-6703.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/6862","paper_id":"site-2643","number":"6862","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wartość wyrażenia log k + \\log{1/100}k² - \\log{1/10}k^3, gdzie k>0, jest równa A. 0 B. 1 C. (-1) D. k","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-6862.svg","solution_image":"img/site/2643/rozw-6862.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/6863","paper_id":"site-2643","number":"6863","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczby rzeczywiste x,y,z spełniają następujące warunki: x,y,z > 0 oraz x,y,z ≠ 1 oraz y^z = x Z podanych warunków wynika, że prawdziwe są równości A. log_x y = z B. y^{-log_y x} = 1/x C. log_x z = y D. y^{log_x y} = x E. log_y x = z F. z^{-log_x z} = 1/y","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-6863.svg","solution_image":"img/site/2643/rozw-6863.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2643/zad/8139","paper_id":"site-2643","number":"8139","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Liczba log_8 4 + log_8 32 - log_8 2 jest równa A. log_8 34 B. 2 C. 3 D. 8","answer":null,"answer_text":null,"solution":null,"image":"img/site/2643/zad-8139.svg","solution_image":"img/site/2643/rozw-8139.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}