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log a 0,5 = 3 a=?

 15.06.2015

Beste Antwort 

 #1
avatar+14537 
+3

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 !

 15.06.2015
 #1
avatar+14537 
+3
Beste Antwort

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 !

radix 15.06.2015
 #2
avatar+12493 
0

Omi67 18.06.2015

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