Question

como resolve log √8 na base √32

Answer 1

$log_{\sqrt{32}}\sqrt{8} = x \\\\ (\sqrt{32})^{x} = \sqrt{8} \\\\ (32^{\frac{1}{2}})^{x} = 8^{\frac{1}{2}} \\\\ (2^{5})^{\frac{x}{2}} = (2^{3})^{\frac{1}{2}} \\\\ \not 2^{\frac{5x}{2}} = \not 2^{\frac{3}{2}} \\\\ \frac{5x}{2} = \frac{3}{2} \\\\ \boxed{x = \frac{3}{5}}$

Answer 2

fatorando, temos

log(√2)³ na base(√2)elevado 5

pelas propriedades dos logaritmos, ficamos com:

3/5•log√2 na base √2
= 3/5•1

= 3/5