化简：（log2(3)+log4(9)+log8(27)+…+log2n(3^n))*log2(8的n次方根)

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/10 13:54:46

A=m^k,B=n^k,则logA(B)=logm(n)
8^(1/n)=(2*2*2)^(1/n)=2^(3/n),故 log2(8^(1/n))=3/n
所以 log2(3)+log4(9)+log8(27)+…+log(2^n)(3^n)=n*log2(3)
所以 (log2(3)+log4(9)+log8(27)+…+log(2^n)(3^n))*log2(8^(1/n))=3*log2(3)

化简：（log2(3)+log4(9)+log8(27)+…+log2n(3^n))*log2(8的n次方根) (log2 3+log4 9+log8 27+...+log2^n 3^n）log9 32的N次方根计算（log2 3+log4 9+log8 27+……+log2^n 3^n）log9 n次根号3 (log2 3+log4 9+.+以2的n次方为底3的n次方的对数）乘以log9 8的n次方根 (log2 3+log4 9.+log8 27+.+log(2^n底)(3^n))log9 n次根号32 (log2（3）+log4（9）+……+log2^n（3^n）)·log9（n次根号8）= log8(9)*log2(3) log3^36-log3^4+log2(log2^16)+8^2/3+(27/8)^-1/3+log8^27/log4^ (log4^3+log8^3)*(log3^2+log9^2)-log2^4次√32 log8的27除以log2的3 log8^9/log2^3的值是 log8 9/log2 3的值是?