Logarithmische Gleichung – Mathe Solutions

375c – FW Algebra

$\ln(2t+1)-\ln(t)=1$

Lösung

$\begin{eqnarray*} \ln\!\left(\frac{2t+1}{t}\right) & = & 1 \mid e^{\wedge} \\ \frac{2t+1}{t} & = & e^1 \\ 2t+1 & = & e\cdot t \\ \left(2-e\right)t & = & -1 \\ t & = & \frac{1}{e-2} \end{eqnarray*}$

374b – FW Algebra

$\lg(u-5)=\lg(u)-\lg(5)$

Lösung

$\begin{eqnarray*} \lg(u-5) & = & \lg\!\left(\frac{u}{5}\right) \mid 10^{\wedge} \\ u-5 & = & \frac{u}{5} \\ 5u-25 & = & u \\ 4u & = & 25 \\ u & = & 6.25 \end{eqnarray*}$

$\begin{eqnarray*} \lg(2)+\lg(a)-2\cdot\lg(a) & = & 0.1 \\ \left(1-2\right)\cdot\lg(a) & = & 0.1-\lg(2) \\ -\lg(a) & = & \lg(10^{0.1})-\lg(2) \\ \lg(a) & = & \lg(2)-\lg(10^{0.1}) \\ \lg(a) & = & \lg\!\left(\frac{2}{10^{0.1}}\right) \mid 10^{\wedge} \\ a & = & \frac{2}{\sqrt[10]{10}} \end{eqnarray*}$

Schlagwort: Logarithmische Gleichung

375c – FW Algebra

Lösung

374b – FW Algebra

Lösung

375a – FW Algebra

Lösung