log以5为底3分之一的对数xlog以5为底4的立方根的对数分之log以5为底根号2的对数xlog以7为底9的对数

[log(5)(根号2)*log(7)9]/[log(5)(1/3)*log(5)(4的立方根)]
={[lg(根号2)/lg5]*(lg9/lg7)}/{[lg(1/3)/lg5]*[lg4的立方根/lg5] 换底公式
=[(1/2)lg2*(2lg3)/(lg5*lg7)]/[(-lg3*lg5)/(2/3)*lg2*lg5]
=(-3/2)*(lg2*lg3*lg5*lg5)/(lg5*lg7*lg3*lg2)
=-3/2*lg5/lg7
=-3/2*log(7底)5