已知已知log8(a)+log4(b^2)=5,log8(b)+log4(a^2)=7,求log4(根号下ab)

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已知已知log8(a)+log4(b^2)=5,log8(b)+log4(a^2)=7,求log4(根号下ab)

已知已知log8(a)+log4(b^2)=5,log8(b)+log4(a^2)=7,求log4(根号下ab)
已知已知log8(a)+log4(b^2)=5,log8(b)+log4(a^2)=7,求log4(根号下ab)

已知已知log8(a)+log4(b^2)=5,log8(b)+log4(a^2)=7,求log4(根号下ab)
log8(a)+log4(b^2)=5===>1/3*log2(a)+log2(b)=5---------1)
log8(b)+log4(a^2)=7===>1/3*log2(b)+log2(a)=7---------2)
解1),2)得:
log2(a)=6
log2(b)=3
log4(根号下ab)=1/4*log2(ab)=1/4×[log2(a)+log2(b)]=9/4