loga logb=log2

(1)y=log2(x^2)-log2(x)=2log2(x)-log2(x)=log2(x)y'=1/(xln2)(2)y=-2sin(x/2)(-cos(x/2)).余弦二倍角公式=2sin(x/

令x=2^log2^(-3)则log2(x)=log2(-3)X=-3

log2[根号下(7/48)]+log2(12)-1/2log2(42)-1?=log2{12*根号下(7/48)/[根号下(42)]}-1=log2{12*根号下[7/(48*42)]}-1=log

根据换底公式log236=a,log210=b可以得到2(lg2+lg3)/lg2=a,lg10/lg2=b,得到lg2=1/b,lg3=(a-2)/2b,log215=lg15/lg2=(lg3+l

log(2)5+log(2)1/10=log(2)(5×(1/10))=log(2)2=1

log2(0.5)=log2(1/2)=log2{2ˆ(-1)}=-1log4(0.5)=log2²(0.5)=1/2log2(0.5)=-1/2-log2(0.5)=1log2(

log2^x=log4^9=log2^2(3^2)=log2^3所以x=3

如果log4(log2^x)是表示外面的log以4为底,而里面的log以10或其它数(>0)为底的话,则log4(log2^x)=[log2(log2^x)]/2=log2(log4^x)=log2(

方法一(log89/log23)=(lg9/lg8)/(lg3/lg2)=(2lg3/3lg2)/(lg3/lg2)=(2/3)*(lg3/lg2)/(lg3/lg2)=2/3方法二(log89/lo

y=lnx/ln2∴y‘=1/(xln2)

log2(2-x)=log2(x-1)+log(2)log2(2-x)=log2[2(x-1)]2-x=2x-2x=4/3带入检验,成立所以x=4/3

log2(x+14)-log2(x+6)=3-log2(x+2)∴log2[(x+14)/(x+6)]=log2[8/(x+2)]∴(x+14)/(x+6)=8/(x+2)且(x+14)/(x+6)>

[log2(-x)]2-log2((-x)2)>=0so[log2(-x)]2-2*log2(-x)>=0solog2(-x)>=2orlog2(-x)=2,-x>=4,x

没有错...换底公式的运用于逆运用.log(2)(3)xlog(3)(7)=ln3xln7/ln2xln3=ln7/ln2=log(2)(7)

log2^9/5底数是2真数是9/5换个写法:LOG(n,m)表示以m为底n的对数LOG(9/5,2)=LOG(9,2)-LOG(5,2)=2*LOG(3,2)-LOG(5,2)=2A-

a=log2(36)=2log2(6)=2log2(2)+2log2(3)log2(3)=(a-2)/2b=log2(10)=log2(2)+log2(5)log2(5)=b-1log2(15)=lo

log(2,9)=log(2,3^2)=2log(2,3)log(2,8)=log(2,2^3)=3log(2,2)=3所以(log2,9)/(log2,8)=2/3(log2,3)

log2(a1a2*……*a2009)=2009a1a2*……*a2009=2^2009a1a2009=a2a2008=……=a1004a1006=(a1005)²所以a1a2*……*a20

log2(x+3)+log2(x+2)=1log2{(x+3)*(x+2)}=1(x+3)*(x+2)=2x^2+5x+4=0(x+4)(x+1)=0所以x=-4或-1因为x+3>0x+2>0所以x>

时,y有最小值为-1/4当t=3即x=8时,y有最大值为2.参考资料：我教高一数学.y=log2(x/4)*log2(x/20=log2(3x/