Question

If a^x = b^y = c^z
then x^a = y^b = z^c =​

Answer 1

Step-by-step explanation:

Let a

x

=b

y

=c

z

=λ, then

log

a

λ=x,log

b

λ=y and log

c

λ=z

Since, x,y and z are in GP

∴y

2

=xz

⇒(log

b

λ)

2

=(log

a

λ)(log

c

λ)

⇒

log

a

λ

log

b

λ

=

log

b

λ

log

c

λ

⇒

log

λ

b

log

λ

a

=

log

λ

c

log

λ

b

(∵log

n

m=

log

m

n

1

)

⇒log

b

a=log

c

b

⇒log

b

a=

log

b

c

1

⇒log

b

alog

b

c=1.