If a^x = b^y = c^z
then x^a = y^b = z^c =
Answers
Answered by
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.
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