$$ \left.\begin{array}{l} a) \displaystyle{\log_{2}(16)} & b) \displaystyle{\log_{2}(0'125)} & c) \displaystyle{\log_{6}(\frac{1}{216})} \\ d) \displaystyle{\log_{5}(0'04)} & e) \displaystyle{\ln(e^{12})} & f) \displaystyle{\ln(e^{-\frac{1}{4}})} \\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) 4 & b) -3 & c) -3 \\ d) -2 & e) 12 & f) -\frac{1}{4}\\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) \displaystyle{\log_{2}(\frac{M \cdot N}{4})} & b) \displaystyle{\log_{2}(\frac{2\sqrt{M}}{N^3})} \\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) 0'1 & b) 6'95 \\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) \displaystyle{\ln(M)+2\ln(N)-\ln(P)} \\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) \ln(\frac{M \cdot N^2}{P})\\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) \displaystyle{\ln(y)=x+\ln(7)} & b) \displaystyle{\ln(y)=2x-\ln(5)}\\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) y=7e^x & b) y=\frac{e^{2x}}{5} \\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) \displaystyle{\log(3000)} & b) \displaystyle{\log(50)} & c) \displaystyle{\log(\sqrt[5]{60})} & d) \displaystyle{\log(\sqrt{\frac{9}{8}})} & e) \displaystyle{\log(0'0012)} \\ \end{array}\right. $$

$$ \left.\begin{array}{l} a) 1'431 & b) 1'699 & c) 0'3556 & d) 0'0255 & e) -2'921 \\ \end{array}\right. $$

Logaritmos:

$$ \left\{\begin{array}{c} \hbox{Dados } a,b>0, a \neq 1, \hbox{ } \log_{a}{b} = x \Leftrightarrow a^x = b\\ \\ \mathbf{\hbox{(Propiedades)}} \left\{\begin{array}{ll} \log_{a}{1} = 0 \hbox{ , } \log_{a}{a} = 1 & \log_{a}{a^n} = n \\ \log_{a}{(x \cdot y)} = \log_{a}{x} + \log_{a}{y} & \log_{a}{\left( \frac{x}{y} \right)} = \log_{a}{x} - \log_{a}{y} \\ \log_{a}{x^n} = n \log_{a}{x} & \log_{a}{\sqrt[n]{x}} = \frac{1}{n} \log_{a}{x} \\ \end{array}\right.\\ \\ \mathbf{\hbox{(Notación)}} \left\{\begin{array}{l} \log_{10}{x} = \log{x} \hbox{ (Logaritmo decimal)} \\ \log_{e}{x} = \ln{x} \hbox{ (Logaritmo neperiano)} \\ \end{array}\right.\\ \mathbf{\hbox{(Cambio de base)}} \left.\begin{array}{l} \\ \log_{a}{x} = \frac{\log_{b}{x}}{\log_{b}{a}} = \frac{\log{x}}{\log{a}} = \frac{\ln{x}}{\ln{a}} \\ \\ \end{array}\right.\\ \mathbf{\hbox{(Exponencial y Logaritmo)}} \left.\begin{array}{ll} \hbox{Dados } a,b>0, a,b \neq 1, & a^x = e^{x \cdot \ln(a)} = b^{x \cdot \log_{b}{a}} \\ \end{array}\right.\\ \end{array}\right. $$