Question

If a = log(2/3) , b = log(3/5) and c = 2 log √(5/2) find the value of a+b+c.

Answer 1

If a = log (2/3) , b = log (3/5) and c = 2 log √(5/2) , then the value of a+b+c = 0.

• Given,

a = log (2/3) , b = log (3/5) and c = 2 log √(5/2)

• Therefore,

a + b + c = log (2/3) + log (3/5) + 2 log √(5/2)

Or, (log 2 - log 3) + (log 3 - log 5) +

[ log {√(5/2) }² ]

(Applying log (a/b) = log a - log b in the first two terms, and

a log b = log bᵃ in the third term)

Or, log 2 - log 3 + log 3 - log 5 +

log (5/2)

(Applying (√a)² = a in the third term)

Or, log 2 - log 5 + (log 5 - log 2)

(Applying log (a/b) = log a - log b in the third term)

Or, log 2 - log 5 + log 5 - log 2

Or, 0