(2/3)^x = 27/8 ?

Hallo Anonymous,

mit dem Potenzvergleich erhälst Du den exakten Wert.

Hallo Anonymous,

$${\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{x}}} = \left({\frac{{\mathtt{27}}}{{\mathtt{8}}}}\right)$$

x*log(2/3) = log(27/8)

$${\mathtt{x}} = {\frac{{log}_{10}\left({\frac{{\mathtt{27}}}{{\mathtt{8}}}}\right)}{{log}_{10}\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}}$$           =>      $${\frac{{log}_{10}\left({\frac{{\mathtt{27}}}{{\mathtt{8}}}}\right)}{{log}_{10}\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}} = -{\mathtt{2.999\: \!999\: \!999\: \!999\: \!999\: \!4}}$$      = -3

oder so:   $${\frac{\left({\mathtt{log27}}{\mathtt{\,-\,}}{\mathtt{log8}}\right)}{\left({\mathtt{log2}}{\mathtt{\,-\,}}{\mathtt{log3}}\right)}} = -{\mathtt{3.000\: \!000\: \!000\: \!000\: \!001}}$$

Gruß radix !

Exponentenvergleich ist weniger aufwendig.