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loga/b-c=logb/c-a=logc/a-b,then the value of a^a.b^b.c^c is equal to

loga/b-c=logb/c-a=logc/a-b,then the value of a^a.b^b.c^c is equal to

Grade:11

1 Answers

NIKHIL GHODKE
55 Points
3 years ago

let us consider every ratio is equal to some constant k

loga/b-c=logb/c-a=logc/a-b=k

then 

loga=k(b-c)

logb=k(c-a)

logc=k(a-b)

now multiply  equation by a,b,c respestively

aloga=k(ab-ac)

blogb=k(bc-ab)

clogc=k(ac-bc)

add all the three equations

we get 

aloga+blogb+clogc=k(ab-ac+bc-ab+ac-bc)

log(aabbcc)=0

s0

aabbc=1

simple right

plzzz approve it means a lot to me

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