若log3^4乘log4^8乘log3^m=log4^2,求m?
问题描述:
若log3^4乘log4^8乘log3^m=log4^2,求m?
答
log3^4乘log4^8乘log3^m=log4^2
2log3(2)*3/2*log2(2)*log3(m)=1/2*log2(2)
3*log3(2)*log3(m)=1/2
log3(m)=1/[6log3(2)]
m=3^{1/[6log3(2)]}
=3^[log64(3)]