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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).
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
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 = 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 if you like the answer please click below on approve
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
if you like the answer please click below on approve
in the explantion above(x-y2)(x+y2)=9 we have to find two factors of 9 which are integersGiven that a and c are integersis it neccessary for (x-y2 ) and (x+y2 ) to be integers???????????????
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