wie berechne ich x bei Gleichung: a hoch x = b

Hallo Anonymous,

$${{\mathtt{a}}}^{{\mathtt{x}}} = {\mathtt{b}}$$         Gleichung logarithmieren !

 x*log(a) = log(b)       =>      $${\mathtt{x}} = {\frac{{log}_{10}\left({\mathtt{b}}\right)}{{log}_{10}\left({\mathtt{a}}\right)}}$$

Zahlenbeispiel:   $${{\mathtt{2}}}^{{\mathtt{5}}} = {\mathtt{32}}$$          ;     $${{\mathtt{2}}}^{{\mathtt{x}}} = {\mathtt{32}}$$     ;         x=   $${\frac{{log}_{10}\left({\mathtt{32}}\right)}{{log}_{10}\left({\mathtt{2}}\right)}} = {\mathtt{5}}$$

Gruß radix !