Question

Sejam a e b reais positivos tais que: log raiz de 5 a = 2010 e log 5 raiz de 5 b = 2020. Qual é o valor de b/a?

Answer 1

log_(V5)a=2010
log_(5^1/2)a=2010

(5^1/2)^2010=a
5^1005=a


log_(5V5)b=2020
log_(5^1×5^1/2)b=2020
log_(5^3/2)b=2020

(5^3/2)^2020=b
5^3030=b

b/a
5^3030/5^1005
5^(3030-1005)
5^2025