Question

5 power x=0.5whole power y=1000 then 1/x-1/y

Answer 1

Answer:

Step-by-step explanation:

I think your question is --> 5^x = (0.5)^y = 1000 find (y - x)/(xy)= ?

it is given that , 5^x = (0.5)^y = 1000

now 5^x = 1000 = (10)³

taking log base 10 both sides,

⇒ log10 (5^x) = log10 (10³)

⇒

⇒ [as we know,  ]

⇒(1)

similarly, (0.5)^y = 1000

⇒ (1/2)^y = 10³

⇒2^-y = 10³

taking log base 10 both sides,

⇒

⇒y=

now, (y-x) =  

=  

= (1)

and xy =  

=(2)

now, from equations (1) and (2),

(y - x)/xy =  

= 1/3

hence, (y - x)/xy = 1/3