Question

If logb(a)=logc(b)=loga(c) then

Answer 1

Answer:

00000000000000900000000000

Answer 2

Answer:

the answer in given step-by-step explanation

Step-by-step explanation:

We can write logba=logalogb and similarly logca=logalogc. Expanding like this, we have,

logbalogca+logablogcb+logaclogbc=3

⇒(loga)2logblogc+(logb)2logalogc+(logc)2logalogb=3

⇒(loga)3+(logb)3+(logc)3logalogblogc=3

⇒(loga)3+(logb)3+(logc)3=3logalogblogc...(1)

Let loga=x,logb=y,logc=z. Then equation (1) transforms to

x3+y3+z3=3xyz⇔x+y+z=0

Then,

loga+logb+logc=0

⇒logabc=0

⇒abc=100=1

hope it's helpful for you