Question

determine o valor de x. w, sabendo que z=log6 27. log 3 36 e w log4 10. log raiz de 16 ao cubo

Answer 1

$\boxed{z=\log_6{27}\cdot\log_3{36}}\\\\\boxed{w=\log_4{10}\cdot\log{\sqrt[3]{16}}}$

$z=\log_627\cdot\log_336\\\\z=\frac{\log27}{\log6}\cdot\frac{\log36}{\log3}\\\\z=\frac{3\log{3}\cdot2\log{6}}{\log{6}\cdot\log{3}}\\\\z=3\cdot2\\\\\boxed{z=6}$

$w=\log_4{10}\cdot\log{\sqrt[3]{16}}\\\\w=\frac{\log{10}}{\log4}\cdot\frac{\log{16}}{3}\\\\w=\frac{1}{2\log2}\cdot\frac{4\log2}{3}\\\\\boxed{w=\frac{2}{3}}$

$\boxed{z\cdot w}\\\\6\cdot\frac{2}{3}\\\\\boxed{\boxed{4}}$