(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_数学解答

(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

人气：481 ℃　时间：2019-10-10 04:55:59

解答

log(2^n)(3^n)=n/nlog2 3=log2 3
log(9) 8^(1/n)=1/n*log9 8
原式
=(log2 3+log2 3+...+log2 3)*1/n*log9 8
=nlog2 3*1/n*log9 8
=lg3/lg2*lg8/lg9
=lg3/lg2*3lg2/(2lg3)
=3/2