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