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Mathematical problems (logarithm)
Solution: Take logarithms from 2 6a = 3 3b = 6 2c, and get 6AlN2 = 3BLN3 = 2LN6.

That is, A/B = LN3/(2LN2) A/C = LN6/(3LN2) A/C× 3-LN2/LN2 = A/B× 2.

∴3ab=2ac+bc

Take the logarithm from a x = b y = c z, and get xlna=ylnb=zlnc.

∴x=(ylnb)/lna z=(ylnb)/lnc

Substitute1/x+1/y+1/z = 0 to get lna/(ylnb)+1/y+lnc/(ylnb) = 0, and multiply both sides of the equation by ylnb to get it.

lna+lnb+lnc=0

∴abc= 1