Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

If x=1+log a bc, y=1+log b ac, z=1+log c ab, Prove that xy+yz+zx = xyz answer it fassstttt

If x=1+logabc, y=1+logbac, z=1+logcab, Prove that xy+yz+zx = xyz
answer it fassstttt

Grade:12

1 Answers

Vikas TU
14149 Points
one year ago
Dear student 
x = 1 + loga (bc)
= loga (a) + loga (bc)
= loga (abc)
or, 1/x = log(abc) a .....(1)
similarly, y = 1 + logb (ca) = logb (abc)
or, 1/y = log(abc) b ......(2)
and z = 1 + logc (ab) = logc (abc)
or, 1/z = log(abc) c ......(3)
now, 1/x + 1/y + 1/z = log(abc) a + log(abc) b + log(abc) c
= log(abc) (a × b × c)
= log(abc) (abc)
= 1
or, 1/x + 1/y + 1/z = 1
or, (yz + yz + xy)/xyz = 1
or, xyz = xy + yz + zx
hence, xyz = xy + yz + zx

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free