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).

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).

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert

b = a^3/2  ;   d= c^5/4

let  a^1/2 = x   and c^1/4 =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

if you like the answer please click below on approve