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LOGARITMI

LOGARITMI. Eksponenttiyhtälön 10 x = a ratkaisua sanotaan luvun a logaritmiksi Merkintä x = lga Huom. vain positiivisilla luvuilla on logaritmi. E.1. a) 10 x = 100 000 10 x = 10 5 x = 5 ”Luvun 100 000 logaritmi on 5” tai x = lg 100 000 x = 5.

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LOGARITMI

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  1. LOGARITMI Eksponenttiyhtälön 10x = a ratkaisua sanotaan luvun a logaritmiksi Merkintä x = lga Huom. vain positiivisilla luvuilla on logaritmi

  2. E.1. a) 10x = 100 000 10x = 105 x = 5 ”Luvun 100 000 logaritmi on 5” tai x = lg 100 000 x = 5

  3. b) 10x = 500 x = lg 500 x  2,70 ”Luvun 500 logaritmi on n. 2,70” E.2. Mikä on luku, jonka logaritmi on a) 4 b) -3 a) 104 = 10 000 b) 10-3 = 0,001

  4. Yhtälön 10x = a ratkaisu on siis lga Jolloin 10 lga = a (a > 0) E.3.Esitä luku 400 kymmenen potenssina 400 = 10lg400  102,60

  5. E.4. (t. 281) Kumpi luvuista 101310 ja 121210 on suurempi? 121210 = (10 lg12)1210 = 10 lg12  1210  10 1306 10 1310 > 10 1306 V: 101310 on suurempi

  6. Kirjan esimerkki 9

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