wie rechne ich den Logarithmus aus dem Bruch : (1/5.wurzelvon64) zur basis 4 aus

$${\frac{{\mathtt{1}}}{{\sqrt[{{\mathtt{{\mathtt{5}}}}}]{{\mathtt{64}}}}}} = {\mathtt{0.435\: \!275\: \!281\: \!648\: \!062\: \!1}}$$

log(x) zur Basis 4 =    $${\frac{{ln}{\left({\mathtt{x}}\right)}}{{ln}{\left({\mathtt{4}}\right)}}}$$      =  $$\left({\frac{{ln}{\left({\frac{{\mathtt{1}}}{{\sqrt[{{\mathtt{{\mathtt{5}}}}}]{{\mathtt{64}}}}}}\right)}}{{ln}{\left({\mathtt{4}}\right)}}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{5}}}} = -{\mathtt{0.6}}$$

Gruß radix !

So kann man es auch rechnen.