3 szkoły ponadpodstawowej

III liceum

III technikum

MATeMAtyka 3. Zakres podstawowy

a) Z tablic logarytmów odczytujemy, że: 0,7168≈log5,21   Zatem:

a) 2,43⋅3,74=10log2,43⋅10log3,74≈100,3856⋅100,5729=100,3856+0,5729=100,9585≈10log9,09=9,09

a) log(310<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​105​)−log310<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​log105​=    =log(1031​105​)−log1031​5​=   =log105−31​−31​5​=

<table style="height:112px;width:1109px;border-collapse:collapse;background-color:#dcdcdc;" border="0"> <tbody> <tr style="height:104px;"> <td style="width:1104.38px;height:104px;"> Niech a&gt;0, b&gt;0 oraz a≠1. Logarytmem o podstawie a z liczby b nazywamy wykładnik potęgi, do której należy podnieść podstawę a, by otrzymać liczbę logarytmowaną b. loga​b=c, gdy ac=b &nbsp; &nbsp; Z powyższej definicji wynika następująca własność, z której będziemy korzystać: aloga​b=b &nbsp; </td> </tr> </tbody> </table> <hr> a) 10log0,01=0,01 &nbsp;

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M834 80h400000v40h-400000z'/></svg>​​(10<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​2⋅10−1<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119
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M834 80h400000v40h-400000z'/></svg>​​(10<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​2⋅10<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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