{"id":4764,"date":"2022-09-02T14:00:12","date_gmt":"2022-09-02T12:00:12","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-3\/"},"modified":"2022-09-02T14:00:12","modified_gmt":"2022-09-02T12:00:12","slug":"rovnice-priklad-3","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-3\/","title":{"rendered":"Rovnice &#8211; p\u0159\u00edklad 3"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Ke ka\u017ed\u00e9 rovnici p\u0159i\u0159a\u010fte interval (A-E), v n\u011bm\u017e je obsa\u017eeno \u0159e\u0161en\u00ed rovnice, p\u0159\u00edpadn\u011b pr\u00e1zdn\u00e1 mno\u017eina (F), pakli\u017ee rovnice nem\u00e1 \u0159e\u0161en\u00ed. Rovnice jsou \u0159e\u0161en\u00e9 v oboru <em><strong>R<\/strong><\/em>.<br \/>&nbsp; <br \/>Rovnice k vy\u0159e\u0161en\u00ed:<br \/>$$1) 3^{2x}=9^{-x}$$<br \/>$$2) 2^{2x}\\cdot 2^{-x}=\\frac{1}{2}$$<br \/>$$3) log(x-2)=log(1-x)$$<br \/>$$4) 2\\cdot logx=1$$<br \/>&nbsp; <br \/>Intervaly pro p\u0159i\u0159azen\u00ed \u0159e\u0161en\u00ed rovnic:<br \/>A) (-\u221e; -1\u232a<br \/>B) (-1; 1\u232a<br \/>C) (1; 2\u232a<br \/>D) (2; 3\u232a<br \/>E) (3; +\u221e)<br \/>F) \u00f8<\/p>\n<p><br data-mce-bogus=\"1\"><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p><em>P\u0159\u00edklad 1<\/em> <br \/>1) Rovnici uprav\u00edme<br \/>$$3^{2x}=9^{-x}$$<br \/>$$3^{2x}=3^{-2}x$$<br \/>2) 3 na obou stran\u00e1ch se n\u00e1m vyru\u0161\u00ed<br \/>$$2x=-2x$$<br \/>3) Nezn\u00e1m\u00e9 se\u010dteme a \u010d\u00edslo p\u0159evedeme na druhou stranu, v tomto p\u0159\u00edpad\u011b zde \u017e\u00e1dn\u00e9 nen\u00ed, tak tam bude 0<br \/>$$4x=0$$<br \/>4) P\u0159epo\u010d\u00edt\u00e1me pro 1x, \u010d\u00edslo se v tomto p\u0159\u00edpad\u011b nezm\u011bn\u00ed<br \/>$$x=0$$<br \/><strong>P\u0159\u00edklad 1 pat\u0159\u00ed do intervalu (B), tj. (-1; 1\u232a<\/strong><\/p>\n<p><em>&nbsp; P\u0159\u00edklad 2<\/em> <br \/>1) Levou stranu rozn\u00e1sob\u00edme, pravou p\u0159evedeme do jin\u00e9ho tvaru<br \/>$$2^{2x}\\cdot 2^{-x}=\\frac{1}{2}$$<br \/>$$2x=2^{-1}$$<br \/>2) P\u0159epo\u010d\u00edt\u00e1me pro 1x<br \/>$$x=-1$$<br \/><strong>P\u0159\u00edklad 2 pat\u0159\u00ed do intervalu (A), tj. (-\u221e; -1\u232a<\/strong><\/p>\n<p><em>&nbsp; P\u0159\u00edklad 3<\/em> <br \/>1) Na obou stran\u00e1ch vyru\u0161\u00edme log<br \/>$$log(x-2)=log(1-x)$$<br \/>$$x-2=1-x$$<br \/>2) Nezn\u00e1m\u00e9 p\u0159evedeme na jednu stranu a \u010d\u00edsla na druhou<br \/>$$2x=3$$<br \/>3) P\u0159epo\u010d\u00edt\u00e1me pro 1x<br \/>$$x=1,5$$<br \/><strong>P\u0159\u00edklad 3 pat\u0159\u00ed do intervalu (F), tj. \u00f8<\/strong><\/p>\n<p><em>&nbsp; P\u0159\u00edklad 4<\/em> <br \/>1) Zbav\u00edme se 2 na lev\u00e9 stran\u011b tak, \u017ee s n\u00ed vyd\u011bl\u00edme \u010d\u00edslo na prav\u00e9 stran\u011b<br \/>$$2\\cdot logx=1$$<br \/>$$log(x)=-0,5$$<br \/>2) Vypo\u010d\u00edt\u00e1me x<br \/>$$x=\\sqrt{10}$$<br \/><strong>P\u0159\u00edklad 4 pat\u0159\u00ed do intervalu (E), tj. (3; +\u221e)<\/strong><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 7-9 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4764","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Rovnice - p\u0159\u00edklad 3 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-3\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rovnice - p\u0159\u00edklad 3 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Ke ka\u017ed\u00e9 rovnici p\u0159i\u0159a\u010fte interval (A-E), v n\u011bm\u017e je obsa\u017eeno \u0159e\u0161en\u00ed rovnice, p\u0159\u00edpadn\u011b pr\u00e1zdn\u00e1 mno\u017eina (F), pakli\u017ee rovnice nem\u00e1 \u0159e\u0161en\u00ed. Rovnice jsou \u0159e\u0161en\u00e9 v oboru R.&nbsp; Rovnice k vy\u0159e\u0161en\u00ed:$$1) 3^{2x}=9^{-x}$$$$2) 2^{2x}cdot 2^{-x}=frac{1}{2}$$$$3) log(x-2)=log(1-x)$$$$4) 2cdot logx=1$$&nbsp; Intervaly pro p\u0159i\u0159azen\u00ed \u0159e\u0161en\u00ed rovnic:A) (-\u221e; -1\u232aB) (-1; 1\u232aC) (1; 2\u232aD) (2; 3\u232aE) (3; +\u221e)F) \u00f8 \u0158e\u0161en\u00ed: P\u0159\u00edklad 1 ... 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Rovnice jsou \u0159e\u0161en\u00e9 v oboru R.&nbsp; Rovnice k vy\u0159e\u0161en\u00ed:$$1) 3^{2x}=9^{-x}$$$$2) 2^{2x}cdot 2^{-x}=frac{1}{2}$$$$3) log(x-2)=log(1-x)$$$$4) 2cdot logx=1$$&nbsp; Intervaly pro p\u0159i\u0159azen\u00ed \u0159e\u0161en\u00ed rovnic:A) (-\u221e; -1\u232aB) (-1; 1\u232aC) (1; 2\u232aD) (2; 3\u232aE) (3; +\u221e)F) \u00f8 \u0158e\u0161en\u00ed: P\u0159\u00edklad 1 ... 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