Question

If log x/y + log y/x = log (x-y), then
1) x/y=1
2) x+y=1
3) x-y=1
4) x*y=1

Answer 1

log(x/y)+log(y/x)=logx-logy+logy-logx=0
meanslog(x-y)=0
means (x-y)=10^0
i.e x-y=1
so option 3

Answer 2

Answer:

Option c - $x-y=1$

Step-by-step explanation:

To find : If $\log (\frac{x}{y})+\log (\frac{y}{x})=\log (x-y)$ then ?

Solution :

$\log (\frac{x}{y})+\log (\frac{y}{x})=\log (x-y)$

Applying logarithmic property, $\log (\frac{A}{B}=\log A-\log B$

$\log x-\log y+\log y-\log x=\log (x-y)$

Cancel the like terms,

$0=\log (x-y)$

Taking exponential both side,

$x-y=10^0$

$x-y=1$

Therefore, Option c is correct.