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標題:

Maths(HKMO)

發問:

Suppose log x t = 6, log y t = 10 and log z t = 15. Find the value of log xyz t.

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最佳解答:

log t/log x=6, log t/log y=10 and log t/log z=15 so, log x/log t=1/6, log y/log t=1/10 and log z/log t=1/15 log x / log t + log y / log t + log z / log t = 1/6+1/10+1/15 = 10/30 = 1/3 (log x+log y+log z)/ log t =1/3 log xyz / log t = 1/ 3 So, log t / log xyz =3 The value of d is 3.

其他解答:

因log(basex) t= 6, log(base y) t= 10, log(base z) t= 15,且x,y,z,t都大於0 即t=x^6,t=y^10,t=z^15 ==>x=t^(1/6),y=t^(1/10),z=t^(1/15) ==>xyz=t^(1/6+1/10+1/15)=t^(1/3) 則t=(xyz)^3 所以log(base xyz) t=3 即d=3 log(base xyz) t=d