Question

alguém me ajuda no item K​

Answer 1

Lembre que podemos escrever radicais como potencias fracionarias da seguinte forma:

$\rightarrow~\sqrt[b]{a^c}~=~a^{\frac{c}{b}}$

k)

$log_{_{\sqrt[3]{4}}}\sqrt{2^3\sqrt{2}}~=~x\\\\\\log_{_{\sqrt[3]{2^2}}}\sqrt{2^3~.~2^{\frac{1}{2}}}~=~x\\\\\\log_{_{2^{\frac{2}{3}}}}\sqrt{2^{\,3+\frac{1}{2}}}~=~x\\\\\\\sqrt{2^{\frac{7}{2}}}~=~\left(2^{\frac{2}{3}}\right)^x\\\\\\\left(2^{\frac{7}{2}}\right)^\frac{1}{2}~=~2^{\,\frac{2}{3}~.~x}\\\\\\2^{\,\frac{7}{2}~.~\frac{1}{2}}~=~2^{\frac{2}{3}x}\\\\\\2^{\,\frac{7}{4}}~=~2^{\frac{2}{3}x}\\\\\\\frac{7}{4}~=~\frac{2}{3}x\\\\\\x~=~\frac{7}{4}~.~\frac{3}{2}$

$\boxed{x~=~\frac{21}{8}}$