Question

Log de3 raiz de 8 de base 16

Answer 1

 Olá Fábio,
boa tarde!

$\log_{16}3\sqrt{8}=\\\\\frac{\log_{10}3\sqrt{8}}{\log_{10}16}=\\\\\frac{\log\sqrt{9\cdot8}}{\log16}=\\\\\frac{\log\sqrt{72}}{\log2^4}=\\\\\frac{\log72^{\frac{1}{2}}}{4\cdot\log2}=\\\\\left(\frac{1}{2}\cdot\log72\right)\div\left(4\cdot\log2\right)=$

$\\\\\frac{\log72}{2}\times\frac{1}{4\cdot\log2}=\\\\\frac{\log72}{8\cdot\log2}=\\\\\frac{\log(2^3\cdot3^2)}{8\cdot\log2}=\\\\\frac{\log2^3+\log3^2}{8\cdot\log2}=\\\\\frac{3\cdot\log2+2\cdot\log3}{8\cdot\log2}=\\\\\frac{3\cdot0,30+2\cdot0,47}{8\cdot 0,30}=\\\\\frac{0,9+0,94}{2,4}=\\\\\boxed{0,7\bar{6}}$