Let a, b, c, d are positive integers such that log a b = 
and log c d = 
. If (a – c) = 9,
find the value of 
.
Text Solution
Verified by Experts93
(93)
Sol. b 2 = a 3 = k ⇒ b = k 1/2 , a = k 1/3 and d 4 = c 5 = λ⇒ c = λ 1/5 , d = λ 1/4
Now a – c = 9 ⇒ k 1/3 – λ 1/5 = 9
Let k 1/3 = 25, λ 1/5 = 16 ⇒ k = 25 3 = 5 6 and λ = 16 5 = 2 20
⇒ b = (5 6 ) 1/2 = 125, d = (2 20 ) 1/4 = 32
Now a – c = 9 ⇒ k 1/3 – λ 1/5 = 9
let k 1/3 = 25, λ 1/5 = 16
⇒ b = (5 6 ) 1/2 = 125, d = (2 20 ) 1/4 = 32
Now b – d = 125 – 32 = 93
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