已知a^2/3=4/9(a>0)则log2/3 a

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已知a^2/3=4/9(a>0)则log2/3 a

已知a^2/3=4/9(a>0)则log2/3 a
已知a^2/3=4/9(a>0)则log2/3 a

已知a^2/3=4/9(a>0)则log2/3 a
a^(2/3)=4/9=(2/3)^2
∴loga[a^(2/3)]=loga(2/3)^2
∴2/3=2loga(2/3)
∴loga(2/3)=1/3
利用换底公式:
lg(2/3)/lga=1/3
∴lga/lg(2/3)=3
∴log(2/3)(a)=3

a^2/3=4/9(a>0)
则loga(a^2/3)=2/3=loga(4/9)=loga(2/3)^2
=2loga(2/3)
loga(2/3)=1/3
loga(2/3)=log2/3(2/3)/log2/3(a)
=1/log2/3(a)=1/3
log2/3a=3