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log2(5/7)+log根号2根号(56/5)

4^(log2 5)+5^(log 5 √7)=(2^2)^(log2 5)+[(√5)]^(log 5 √7)=2^(log2 25)+(√5)^(log 5 7)=25+7=32

log2底根号5/56+log2(14)-1/2log2(35)=log2(根号5/56*14/根号35)=log2 根号7/28

(log2 5+log4 125)log3 2/ log根号3 5=(log2 5+log4 125)log3 2/ log3 25=(log2 5+log4 125)log25 2=(log2 5+log2 5根号5)log25 2=log2 25根号5 *log25 2=lg2/lg25根号5 *lg25 /lg2 (换底公式)=log25 25根号5=log 5 5的5/2次方=5/4

log7 3倍的根号4, 这个应该是4的开立方原式=log(5,2)log(7,3)/[-log(5,3)log(7,4)/3]+log(2,[根号(3+根号5)根(3-根号5)])=-3log(3,2)log(4,3)+log(2,[根号(3+根号5)根(3-根号5)]^2)/2=-3log(3,2)/log(3,4)+log(2,{(3+根号5)+(3-根号5)-2根号[(3+根号5)(3-根号5)]})/2=-3log(4,2)+log(2,2)/2=-3/2+1/2=-1

=(1/2)log(2)5=(1/2)(lg5/lg2)然后根据常用对数表=(1/2)(0.6990/0.3010)

log2 (5/56)^(1/2)+log2 (14)-(1/2)log2 (35) =1/2log2 (5/56)-1/2log2 (35)+log2 (14) =1/2[log2 (5/56/35)]+log2 (14) =1/2log2 [1/(7^2*8)]+log2 (14) =1/2(log2 [7^(-2)*2^(-3)]+log2(2*7) =1/2[-2log2 (7)-3]+log2 (2)+log2 (7) =-log2 (7)-3/2+1+log2 (7) =-1/2

答案是1.要用到换底公式logA(B)=lnB/lnA那么原式=(ln9/ln2)*(ln(根号5)/ln3)*(ln5/ln2) =2ln3/ln2 * (1/2ln5)/ln3) * ln5/ln2 你自己在稿纸上列式子看得清楚些,上下的都约分了,答案是1

(log5 根号2乘log2 9)÷(log5 1/3乘log7 三次根号下4)=(1/2log5 2乘2log2 3)÷(-log5 3乘2/3log7 2)=(log5 2乘log2 3)÷(-2/3log5 3乘log7 2)=lg2/lg5*lg3/lg2÷(-2/3lg3/lg5*lg2/lg7)=lg3/lg5*(-3/2lg5/lg3*lg7/lg2)=-1.5lg7/lg2

(1)log2(0.3)-log1/2(3)=log2(0.3)+log2(3)=log2(0.3*3)=log2(0.9)<0 所以log2(0.3)(2)根据图像知,在(0,1)上,y=log10(1/2)在y=log2(1/2)上方,所以log10(1/2)>log2(1/2) 还可以:lg(1/2)=1/[log(1/2)10],log2(1/2)=1/[log(1/2)2],因为log(1/2)10log2(1/2)

根号2=2^(1/2)所以log以2为底根号2的对数=0.5 log(2)√2=log(2)2^(1/2)=1/2*log(2)2=1/2=0.5注:(2)是底数

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