✔ 最佳答案
(1)
a^2=bclogA
b^2=calogB
c^2=ablogC
logA+logB+logC
=a^2/(bc)+b^2/(ca)+c^2/(ab)
=(a^3+b^3+c^3)/(abc)
=(a^3+b^3+c^3-3abc)/(abc)+3abc/(abc)
=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)/(abc)+3
=0+3
=3
(2)
Sol
設p=a^[log(b/c)]*b^[log(c/b)]*c^[log(a/b)]
logp=log{a^[log(b/c)]*b^[log(c/b)]*c^[log(a/b)]}
=log{a^[log(b/c)]}+log{b^[log(c/b)]}+log{c^[log(a/b)]}
=loga*log(b/c)+logb*log(c/b)+logc*log(a/b)
=loga*(logb-logc)+logb(logc-logb)+logc(loga-logb)
=0
p=1
(3)
Sol
a^x=b^y=(ab)^z
xloga=ylogb=zlog(ab)=p
1/x+1/y-1/z
=loga/p+logb/p-log(ab)/p
=log1/p
=0