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Let a, b, c, d are integers such that log a b=3/2 and log c d=5/4 . If (a-c)=9 , find (b-d).

Let a, b, c, d are integers such that log a b=3/2 and log c d=5/4.


If (a-c)=9 , find (b-d).

Grade:12

3 Answers

Aman Bansal
592 Points
11 years ago

Dear Deepti,

use the relation,

logb(a) = loge(a) / loge(b)

thus you get two more relations between a,b,c,d and these can bedidivided in log to get log(b-d).

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sanatan sharma
26 Points
11 years ago

b = a3/2  ;   d= c5/4

let  a1/2 = x   and c1/4 =y

then b = x3 and d = y5

given  a-c = 9     or      x2 - y4 = 9     or          (x-y2)(x+y2)=9

we have to find two factors of 9 which are integers

now ; 9 can be expressed as 9x1  or 3x3

i.e. if we breah 9 as 3x3 then x-y2 = x+y2 which is not possible for any existing integer

therefore  x-y2 = 1  and x+y2 = 9 

adiing the two equations we get     2x = 10   or x=5

and if x = 5 then y = 1

therefore b = 125   and  d =32

therefore b-d = 83

 

 

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Ramesh Kn
24 Points
8 years ago
in the explantion  above
(x-y2)(x+y2)=9       we have to find two factors of 9 which are integers
Given that a and c are integers
is it neccessary for   (x-y2 )   and     (x+y2  )                 to be integers???????????????

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