lna+lnb ???? lna-lnb ??_????
...? lna+lnb=ln (ab) lna-lnb=ln (a/b) ???? ????????????ax=N?a>0??a?1?????x???a??N??????x=logaN????a??N??????a????????N???????????y=logax?a>0??a?1??? ???????????? ????????????????????? ......
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ln (a/b)=lna-lnb ln (ab)=lna+lnb????_????
...??? ln (a/b)=lna-lnb?ln (ab)=lna+lnb? ???????? 1?log (a) (M·N?=log (a) M+log (a) N 2?log (a) (M÷N)=log (a) M-log (a) N 3?log (a) M^n=nlog (a) M 4?log (a)b*log (b)a=1 5?log (a) b=log (c) b÷log (c) a ???? ???????? ?1614???????????·?????Jost Bürgi????Jost Bürgi??6??????? ......
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a?x?????? - ????
...?????????? (a^x)'= (lna) (a^x) ????? y=a^x ??????????lny=xlna ?????x??????y'/y=lna ??y'=ylna=a^xlna??? ????? 1?????????????? 2????????????????????????y=|x|?y=0??????...
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lna/lnb??ln (a/b)?-????
...????ln (a/b) = lna - lnb? ???a>0?b>0??ln (a/b)=lna-lnb,ln (ab)=lna+lnb??? ???????? 1?log (a) (M·N?=log (a) M+log (a) N 2?log (a) (M÷N)=log (a) M-log (a) N 3?log (a) M^n=nlog (a) M 4?log (a)b*log (b)a=1 5?log (a) b=log (c) b÷log (c) a ?????? ????y=logax ????? {x ?x>0}??????????? ......
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lna?lnb?????-????
...lna×lnb=ln (a+b)? log????????n???????????????????????????????????10?100?1000? 2?4?8?????????????????????????? ??m=lna?n=lnb? ??a=e^m?b=e^n? a×b= (e^m)× (e^n)=e^ (m?n)? ??ln (a×b)=m?n=lna?lnb? log????? ......
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lna?lnb?????_????
...??? ??m=lna?n=lnb ??a=e^m?b=e^n a×b= (e^m)× (e^n)=e^ (m?n) ??ln (a×b)=m?n=lna?lnb lna×lnb=ln (a+b) ?? ???????????????????????????????????? ?????????????????????????? ??????????????????????? ......
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???a=e^lna?????????????? - ????
...?? ???Ww 2024-04-26 ?? ???e^x = a ???ln?a?= x ????? e^x = a ???? e^lna = a ???????????? x ,?????????? ??...
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lna÷lnb????? - ????
...lna÷lnb=logb?a? ????? loga?N?=[logb?N?]÷[logb?a?]?a?0??a?1?b?0?b?1?N?0? ?????...
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e?ln?log?????????? - ????
...????? n???e???log?lna???loge a? lg???10???log? log (c) (a*b)=log (c)a+log (c)b ???????????,??????????? log (c) (a/b)=log (c)a/log (c)b ???????????,?????????? ? log (c) (a^n)=n*log (c)a ?????????,??????????? ???? ......
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ln (a+b)????_????
...Ln (a + b) = Lna * Ln [1 + (b/a)] = Lnb * Ln [1 + (a/b)] ???????e? ?? ??????lnN (N>0)?????????????????????????????lnx????????logx???????????????10?????lgx??????????ex? ??e????????????????? ......
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