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log2(3)乘log3(8)等于

满意答案用换底公式log2^3=lg2/lg3上式等于(lg2/lg3)*(lg3/lg5)*(lg5/lg7)*(lg7/lg8)=lg2/lg8=log2^8=38=2^3log2^8=3log2^2=3

f(8)=f(√2^6)=log(2)√2=1/2 log(√2-1)(3+2√2)=log(√2-1)(√2+1)^2 =-2 (√2+1=1/(√2-1))

log2+log3=log6 如下图所示,是“4”的第一个公式的逆运算

-log2(3/8)=-log2[3]+log2[8]=3-log2[3]

解 log2(9)×log3(8) =log2(3²)×log3(2³) =2log2(3)×3log3(2) =6×log2(3)×log3(2) =6×1 =6

解:log3 x+ log3 (x+8)=2 log3 x(x+8)=log3 9 x(x+8)= 9 x²-8x-9=0 (x-9)(x+1)=0 x1=9 x2=-1 经检验x=-1是增根,x=9是原方程的根。

应该是log3(2)*log8(3) 2和3是真数所以: log3(2)*log8(3)=log3(2)*log3(3)/log3(2)^3 =log3(2)*1/3log3(2) =1/3 这里用了对数换底公式 loga(b)=logc(b)/logc(a)

对数的化简log8(4)=log(2^3)(2^2)=(2/3)log2(2)=2/3, 即8=2^3,4=2^2,底数的指数3化到系数的分母,真数的指数2化到系数的分子,得到2/3,对数变为log2(2)=1,

方法一 (log8 9/log2 3) =(lg9/lg8)/(lg3/lg2) =(2lg3/3lg2)/(lg3/lg2) =(2/3)*(lg3/lg2)/(lg3/lg2) =2/3 方法二 (log8 9/log2 3) =log2^3 3^2/log2 3 =(2/3)log2 3/log 2 3 =2/3 logm^a n^b =(b/a)logm n

log4(3)+log8(3) =log2(3)/log2(4)+log2(3)/log2(8) =0.5log2(3)+1/3*log2(3) =5/6*log2(3) 在高中阶段运算到这一步化为单个对数就可以了,主要运用的是换底公式。

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