let a , b , c , and d be positive integers such that log base a of b =3/2 and log base c of d = 5/4 . if a - c = 9 then b - d equals to (a) 55 (b) 23 (c) 89 (d) 93
Answers
Answered by
8
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
please mark it as brainliest
pkaramasotpdjil2:
sorry
Answered by
0
Answer:
(d)93
Step-by-step explanation:
Similar questions