log?lg?ln????_????
...log????????????log?2????log?8???2???????????2?3???8???8??2?????3? lg?10????????????? ln?? ???e ?e=2.71828...????????? ???? ??????????????????????????? ????????? ......
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ln?????ln????????-????
...lnx??e??????????e????????????????2.718281828459? ?????????1,0????C????,??????????????????????Y ???????????????????X?? ?????x>0 ???y???? ???? ??????????y=logax ? ......
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ln???????? - ????
...LN????????????????????????????LN?????????? 1?ln (xy)=ln (x)+ln (y)???????????????????????????????????????????...
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?????????_????
...????????? 1.lnx+ lny=lnxy 2.lnx-lny=ln (x/y) 3.lnx?=nlnx 4.ln (??x)=lnx/n 5.lne=1 6.ln1=0 ????? ?????? (rule of logarithmic operations??????????.?????????????????? ???????????????????????????????? ??????????? ......
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ln??????? - ????
...ln???????ln?????????????????1.ln (x)???e???x??????e??2.71828? ??ln?????????...
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??ln?e?????? - ????
...??ln?e?????????????????ln??e???????b=e^a???a=lnb????????e?????????lnN (N>0)?????????????????????????????lnx??????...
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y=ln?x+???1+x^2???? - ????
...y=ln (x+??x^2+1?)?????1/??x^2+1?? ??????? ????? ?h (a)=f [g (x)]??h' (a)=f? [g (x)]g? (x)? ?????????????????????? ?????????????????????????????????? ? ???????...
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y?ln (1+x)?n??? - ????
...????? y'=1/ (1+x)= (1+x)^ (-1) y''=-1* (1+x)^ (-2) y'''=-1* (-2)* (1+x)^ (-3)=2* (1+x)^ (-3) y''''=2* (-3)* (1+x)^ (-4)=-6* (1+x)^ (-4) ?? y^ (n)= (-1)^ (n+1)* (n-1)!* (1+x)^ (-n) ????? ????????????????????????????????????????????? n ???????????????? ......
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ln (1+x)????? - ????
...?????x??????1??????????????0?????????????ln (1+x)??? ?????????????????x??????...
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x??0? ln (1-x)?????? - ????
...??????????????ln (x)?x=1?????? ????ln (1) = 0??????1-x?????1??ln (1-x)??????0? ?????????1????????????????????0? ??????????????????ln (1-x)??? ......
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