Frage: log(0.5) zur Basis a = 3 Wie groß ist a ? Ist das so gemeint ?
$${\frac{{log}_{10}\left({\mathtt{0.5}}\right)}{{log}_{10}\left({\mathtt{a}}\right)}} = {\mathtt{3}}$$ => $${\mathtt{3}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{a}}\right) = {log}_{10}\left({\mathtt{0.5}}\right)$$
$${\mathtt{3}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{a}}\right) = {log}_{10}\left({\mathtt{0.5}}\right) \Rightarrow {\mathtt{a}} = {{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{13\,614\,799}}}{{\mathtt{58\,926\,009}}}}\right)} \Rightarrow {\mathtt{a}} = {\mathtt{0.793\: \!700\: \!525\: \!984\: \!099\: \!6}}$$
Probe: $${\frac{{log}_{10}\left({\mathtt{0.5}}\right)}{{log}_{10}\left({\mathtt{0.793\: \!7}}\right)}} = {\mathtt{2.999\: \!991\: \!395\: \!376\: \!062\: \!2}}$$
Gruß radix 
!
+14538 
!