Simplifique as expressões
Funções exponenciais e logarítmicas: Infinito 12 A - Parte 2 Pág. 48 Ex. 23
Simplifique as expressões:
- $A=\ln e+\ln {{e}^{2}}+\ln {{e}^{3}}$
- $B=\ln e-\ln \left( \frac{1}{e} \right)$
- $C=\ln \left( e\sqrt{2} \right)$
- $D=\ln {{e}^{2}}-2\ln e$
- $E=\ln 3+\ln \left( 27e \right)-\ln \left( 9{{e}^{3}} \right)$
\[\begin{array}{*{35}{l}}
A & = & \ln e+\ln {{e}^{2}}+\ln {{e}^{3}} \\
{} & = & 1+2+3 \\
{} & = & 6 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
B & = & \ln e-\ln \left( \frac{1}{e} \right) \\
{} & = & 1-\ln \left( {{e}^{-1}} \right) \\
{} & = & 1-(-1) \\
{} & = & 2 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
C & = & \ln \left( e\sqrt{2} \right) \\
{} & = & \ln e+\ln \sqrt{2} \\
{} & = & 1+\ln {{2}^{\frac{1}{2}}} \\
{} & = & 1+\frac{1}{2}\ln 2 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
D & = & \ln {{e}^{2}}-2\ln e \\
{} & = & 2-2\times 1 \\
{} & = & 0 \\
\end{array}\]
\[\begin{array}{*{35}{l}}
E & = & \ln 3+\ln \left( 27e \right)-\ln \left( 9{{e}^{3}} \right) \\
{} & = & \ln 3+\ln \left( \frac{27e}{9{{e}^{3}}} \right) \\
{} & = & \ln 3+\ln \left( \frac{3}{{{e}^{2}}} \right) \\
{} & = & \ln 3+\ln 3-\ln {{e}^{2}} \\
{} & = & -2+2\ln 3 \\
\end{array}\]
