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log2(3)乘log3(8)等于

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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))

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

log2+log3=log6 如下图所示,是“4”的第一个公式的逆运算

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

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,

log(2) 3 = 1.5849625007211561814537389439478

log2(9)=log2(3²)=2log2(3) ∴log2(9)×log3(2)=2log2(3)×log3(2) =2×1 =2 望采纳

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

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)

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