Question

If logx/a-b=logy/b-c=logz/c-a then xyz is

Answer 1

Answer:

xyz=1

Step-by-step explanation:

Formula used:

Product rule :

$log\:a+log\:b+log\:c=log\:abc$

$log_a{1}=0$

Given:

$\frac{logx}{a-b}=\frac{logy}{b-c}=\frac{logz}{c-a}=k(say)$

Then,

$\frac{logx}{a-b}=k$

$logx=k(a-b)$..............(1)

$\frac{logy}{b-c}=k$

$logy=k(b-c)$..............(2)

$\frac{logz}{c-a}=k$

$logz=k(c-a)$...............(3)

Adding (1), (2) and (3), we get

$logx+logy+logz=k(a-b)+k(b-c)+k(c-a)$

$logx+logy+logz=k[a-b+b-c+c-a]$

$logx+logy+logz=k[0]$

$logx+logy+logz=0$

$logxyz=0$ (using first formula))

This implies

$xyz=1$ (using second formula)

Answer 2

Answer:

1

Step-by-step explanation: