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# 高中数学公式大全 (2010版全)

*表示乘号，/表示除号

1.a^(log(a)(b))=b
2.log(a)(MN)=log(a)(M)+log(a)(N);
3.log(a)(M/N)=log(a)(M)-log(a)(N);
4.log(a)(M^n)=nlog(a)(M)

1.这个就不用推了吧，直接由定义式可得(把定义式中的[n=log(a)(b)]带入a^n=b)

2.
MN=M*N

a^[log(a)(MN)] = a^[log(a)(M)] * a^[log(a)(N)]

a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}

log(a)(MN) = log(a)(M) + log(a)(N)

3.与2类似处理
MN=M/N

a^[log(a)(M/N)] = a^[log(a)(M)] / a^[log(a)(N)]

a^[log(a)(M/N)] = a^{[log(a)(M)] - [log(a)(N)]}

log(a)(M/N) = log(a)(M) - log(a)(N)

4.与2类似处理
M^n=M^n

a^[log(a)(M^n)] = {a^[log(a)(M)]}^n

a^[log(a)(M^n)] = a^{[log(a)(M)]*n}

log(a)(M^n)=nlog(a)(M)

log(a)(N)=log(b)(N) / log(b)(a)

N = a^[log(a)(N)]
a = b^[log(b)(a)]

N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}

b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}

log(b)(N) = [log(a)(N)]*[log(b)(a)] {这步不明白或有疑问看上面的}

log(a^n)(b^m)=m/n*[log(a)(b)]

log(a^n)(b^m)=ln(a^n) / ln(b^n)

log(a^n)(b^m) = [n*ln(a)] / [m*ln(b)] = (m/n)*{[ln(a)] / [ln(b)]}

log(a^n)(b^m)=m/n*[log(a)(b)]
--------------------------------------------（性质及推导 完 ）

log(a)(b)=1/log(b)(a)

=1/log(b)(a)

log(a)(b)*log(b)(a)=1

sinα＋sinβ＝2sin（α＋β）/2·cos（α－β）/2
sinα－sinβ＝2cos（α＋β）/2·sin（α－β）/2
cosα＋cosβ＝2cos（α＋β）/2·cos（α－β）/2
cosα－cosβ＝－2sin（α＋β）/2·sin（α－β）/2

sinα ·cosβ＝1/2 [sin（α＋β）＋sin（α－β）]
cosα ·sinβ＝1/2 [sin（α＋β）－sin（α－β）]
cosα ·cosβ＝1/2 [cos（α＋β）＋cos（α－β）]
sinα ·sinβ＝-1/2 [cos（α＋β）－cos（α－β）]

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