Gleichung lösen

Hallo Anonymous,

auch ich habe Schwierigkeiten mit der Schreibweise, aber ich hoffe, es geht so:

$${{\mathtt{512}}}^{\left({\frac{{\mathtt{1}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}}\right)}$$ = $${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}$$              ;  512=2^9     ;   2*2^(x-1) = 2^x

$${{\mathtt{2}}}^{\left({\frac{{\mathtt{9}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}}\right)}$$ =  $${{\mathtt{2}}}^{{\mathtt{x}}}$$

$${\frac{{\mathtt{9}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}} = {\mathtt{x}}$$          =>   2x^2-3x = 9     ( quadratische Gleichung )

=>      x = 3    und    x = -1,5

Probe:    $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{512}}}} = {\mathtt{8}}$$       und   $${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{2}}} = {\mathtt{8}}$$

Probe mit x = -1,5  haut auch hin !

x = 3    und   x =-1,5

Wenn du noch Fragen hast, melde dich bitte.

Gruß radix !