Question

Sendo L= log √2 √32 + Log 1/7 1/49, calcule o valor de L.

Por favor expliquem a conta também.

Answer 1

$L=log_{\sqrt{2}}\sqrt{32} + log_{\frac{1}{7}}\frac{1}{49}\\\\ L=log_{\sqrt{2}}\sqrt{2^5} + log_{\frac{1}{7}}(\frac{1}{7^2})\\\\ L=log_{\sqrt{2}}(\sqrt{2})^5 + log_{\frac{1}{7}}(\frac{1}{7})^2\\\\ L=5.log_{\sqrt{2}}(\sqrt{2}) + 2.log_{\frac{1}{7}}(\frac{1}{7})\\\\ L=5.1+2.1=5.2=7$