EKSPONENCIJALNE i LOGARITAMSKE FUNKCIJE

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LOGARITMI www.mim-sraga.com 2. Koliko je: 1) log 8 = x 2) log 27 = x 2 3 x 8 = 2 27 = 3 3 x 3 x 2 2 3 3 = = 3 = x 3 = x x = 3 x = 3 x 3) log 16 = x 4) log 16 = x 2 1 2 x ⎛1 ⎞ 16 = 2 16 = ⎜ ⎟ ⎝2 ⎠ − ( ) 2 = 2 2 = 2 4 x 4 1 = x = 4 − x 4 2 2 x = 4 4 = − x 1 1 2 3 − x − ( ) ( ) 5 1 3 1 5 − x 3 2 2 3 x =−4 5) log 32 = x 6) log 27 = x x ⎛1⎞ ⎛1⎞ 32 = ⎜ ⎟ 27 = ⎜ ⎟ ⎝2⎠ ⎝3⎠ 2 = 2 3 = 3 = = 3 5 =− x 3 =−x x =− 5 x =−3 x − x x x x 7) log 3 = x 8) log 64 = x 9) log 2 = x 1 1 3 2 x ⎛1⎞ ⎛1⎞ 3 = ⎜ ⎟ 64 = ⎜ ⎟ ⎝3⎠ ⎝2⎠ −1 x 6 −1 ( ) ( ) 1 1 2 x 2 3 = 3 2 = 2 2 = 2 1 = = = x 2 1 1 =− x 6 =− x x = 2 2 1 x =− x =−6 2 1 2 −x 6 −x 3 3 2 2 x 2 2 = 2 x x Autor kompletnih rješenja: Mladen Sraga © M.I.M.- Sraga d.o.o. 10
LOGARITMI kompletna rješenja www.mim-sraga.com 3. 1) log x = 4 2) log x = 9 2 3 x = 2 x = 3 x = 16 4 9 3) log x = 2 4) log x = 1 9 2 ( ) 2 ⎛1 ⎞ x = ⎜ ⎟ ⎝2 ⎠ x = 1 x = 4 x = 9 x = 3 1 1 5) log8 x = 6) log3 x = 3 2 ( 9) 1 1 3 2 x = 8 x = 3 x 3 = = x = 2 8 x 3 1 2 1 2 1 7) log2 x = 8) log2 x = 0 3 x = 2 x = 2 x 3 = = 2 x 1 0 1 3 1 2 1 1 9) log0.1 x = 2 10) log25 x = 11) log27 x = 2 3 x = x = 2 0.1 25 2 x = 27 ⎛ 1 ⎞ x = ⎜ ⎟ ⎝10 ⎠ x = x = 1 x = 100 x = 5 x = 3 x = 3 3 25 27 1 3 3 3 11 Autor zadataka: Mladen Sraga
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EKSPONENCIJALNE i LOGARITAMSKE FUNKCIJE

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