Question

determine o valor de log4 ³√2

Answer 1

log4 ³√2

Aplicando as propriedades logarítmicas de potência e soma
$log4^3_{ \sqrt{2}} = 3 log4_{ \sqrt{2}} = 3( \frac{log4}{log \sqrt{2}}) \\\\ \frac{3log4}{log \sqrt{2}} = \frac{3(log2 + log2)}{log \sqrt{2}}$

Sendo log2 ≈ 0,3. Temos que:
$log \sqrt{2} = log2^{1/2} = \frac{1}{2}log2=0,5.0,3=0,15$

Então, voltando a conta:
$\frac{3(log2 + log2)}{log \sqrt{2}} \\\\ \frac{3(0,3+0,3)}{0,15}\\\\\frac{3(0,6)}{0,15}\\\\\frac{1,8}{0,15}\\\\=12$

Ik_Lob