Question

if loga/y-z=logb/z-x=logc/x-y the value of abc is

Answer 1

Answer:

$abc=1$

Step-by-step explanation:

Formula used:

Product rule :

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

$log_a{1}=0$

Given:

$\frac{log\:a}{y-z}=\frac{log\:b}{z-x}=\frac{log\:c}{x-y}=k(say)$

Then,

$\frac{log\:a}{y-z}=k$

$\frac{log\:b}{z-x}=k$

$\frac{log\:c}{x-y}=k$

⇒

$log\:a=k(y-z)$

$log\:b=k(z-x)$

$log\:c=k(x-y)$

Adding these equations, we get

$log\:a+log\:b+log\:c=k(y-z)+k(z-x)+k(x-y)$

$log\:a+log\:b+log\:c=k[y-z+z-x+x-y]$

$log\:a+log\:b+log\:c=k[0]$

$log\:a+log\:b+log\:c=0$

$log\:{abc}=0$ (by using (1))

⇒ $abc=1$ (by using (2))

Answer 2

Answer:

abc=1

Step-by-step explanation:

hope this will help better and u can understand it