5=10^t

Hallo Anonymous,

5=10^t       | logarithmieren

log(5)=t*log(10)          =>     t = log(5)/log(10)

$${\mathtt{t}} = {\frac{{log}_{10}\left({\mathtt{5}}\right)}{{log}_{10}\left({\mathtt{10}}\right)}} \Rightarrow {\mathtt{t}} = {\mathtt{0.698\: \!970\: \!004\: \!336\: \!018\: \!9}}$$

Probe:   $${{\mathtt{10}}}^{{\mathtt{0.698\: \!97}}} = {\mathtt{4.999\: \!999\: \!950\: \!079\: \!738\: \!9}}$$

1,9361=1,045^t        | logarithmieren

log(1,9361)= t*log(1,045)

$${\mathtt{t}} = {\frac{{log}_{10}\left({\mathtt{1.936\: \!1}}\right)}{{log}_{10}\left({\mathtt{1.045}}\right)}} \Rightarrow {\mathtt{t}} = {\mathtt{15.009\: \!595\: \!389\: \!527\: \!665\: \!8}}$$

Probe:    $${{\mathtt{1.045}}}^{{\mathtt{15.009\: \!595\: \!39}}} = {\mathtt{1.936\: \!100\: \!000\: \!040\: \!254\: \!7}}$$

Gruß radix !