Question

Q3.If a^x= b^y= c^z and b^2 =
= ac,
Prove that: y= 2xz/x+z​

Answer 1

Given :

a^x = b^y = c^z , b² = ac

To prove :

y = 2xz/(x + z)

Proof :

Let

a^x = b^y = c^z = k

Thus ,

• If a^x = k , then a = k^(1/x)

• If b^y = k , then b = k^(1/y)

• If c^z = k , then c = k^(1/z)

Also ,

It is given that , b² = ac

=> [ k^(1/y) ]² = [ k^(1/x) ]•[ k^(1/z) ]

=> k^(2/y) = k^(1/x + 1/z)

=> 2/y = 1/x + 1/z

=> 2/y = (z + x)/xz

=> y = 2xz/(x + z)

Hence proved .

Answer 2

Step-by-step explanation:

let a^x=b^y=c^z= k'

where k and k' are constants and >0

a^x= k'

x log a = k

log a = k/x -----A

b^y = k'

y log b=k

log b = k/y -----B

c^z=k'

z log c =k

log c = k/z ------C

b^2=ac

2log b = log ac

(logmn=logm+logn)

2log b = loga+logc ------D

substitute from A,B,C in D

2k k k

__ = __+__

y x z

divide the above equation with k on both sides

2 1 1

__ = __+ __

y x z

2 z + x

__ = ______

y xz

cross multiply

2xz = y(x+z)

y=2xz/(x+z)

hope this helps