Let logab = 4 , logcd=2, a,b,c,d are natural numbers if b-d = 7 then find c-d? ( plz do it fast) ( KVPY 2009 question)

Dear Student,
Please find below the solution to the asked query:

We havelogab=4b=a4...ilogcd=2d=c2....iii-iia4-c2=b-da4-c2=7a2+ca2-c=7×1As a,b,c,d are natural numbers, hencea2+c=7....iiia2-c=1...iviii+iv2a2=8a2=4a=2Put in iii4+c=7c=3d=c2=9c-d=3-9=-6 

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