Assisting with Rules for Po

Mgr Vladimir Wasyliw provides guidance and support in navigating the rules and regulations for engaging in the activity of Po.

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2. (a.b) n = a n . b n a r . a s = a r+s a r : a s = a r-s (a r ) s = a r.s a -r = 1/a r a 0 = 1

3. - Pomoc pravidel pro potn s mocninami upravme rovnice tak, abychom na obou stranch mli mocninu se stejnm zkladem. - Porovnme exponenty na obou stranch rovnice.

4. 8 2x 1 = 2 x 2 3(2x 1) = 2 x 2 6x 3 = 2 x 6x-3 = x 5x = 3 x = 3/5

5. 1/ logaritmus souinu log a (x.y) = log a x + log a y 2/ logaritmus podlu log a x/y = log a x log a y 3/ logaritmus mocniny log a x n = n.log a x 4/ zmna zkladu logaritmu

6. - Pomoc pravidel pro potn s logaritmy upravme rovnici tak, abychom na obou stranch mli logaritmus se stejnm zkladem (jeden) - Porovnme logaritmovan sla

7. log 7 x = log 7 5 + log 7 4 Podle pravidla o logaritmu soutu: log 7 x = log 7 (5.4) x = 20 log 3 x = log 3 10 log 3 2 Podle pravidla o logaritmu rozdlu: log 3 x = log 3 (10/2) x = 5 log 3 x = 4.log 3 10 log 3 x = log 3 10 4 x = 10 000

8. Vraz log a x nahradme jinou promnnou (nap. y) subst: log a x = y Tm rovnici pevedeme na jednodu (nejastji kvadratickou)

9. log 2 3 x 7 log 3 x + 10 = 0 subst. log 3 x = y Dostaneme rovnici y 2 7y + 10 = 0 Rovnice m dv een: y 1 = 2 log 3 x = 2 x 1 = 3 2 = 9 y 2 = 5 log 3 x = 5 x 2 = 3 5 = 243

10. Nelze-li pevst mocniny na stejn zklad, pouijeme tzv. logaritmovn rovnice. Pomoc pravidla o logaritmu mocniny pak pevedeme mocninu na nsobek.

11. 2 x = 5 3 log 2 x = log 5 3 x.log 2 = 3.log 5 x = 3.log 5 log 2 x = 6,966