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

$Log_{ \sqrt{5}}a = 2020 \\ \\ a = \sqrt{5}^{2020} \\ \\ a = 5^{ \frac{2020}{2}} \\ \\ a = 5^{1005} \\ \\ \\ \\ Log_{ (5\sqrt{5})}b = 2020 \\ \\ b = (5 \sqrt{5})^{2020} \\ \\ b = (5.5^{ \frac{1}{2}})^{2020} \\ \\ b = 5^{\frac{3}{2}.2020} \\ \\ b = 5^{3030} \\ \\ \\ \\ b/a = \frac{5^{3030}}{5^{1005}} = 5^{2025}$