Logaritmos

Actividad (#1)

Calcula:

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

Actividad (#2)

Sabiendo que \( \left.\begin{array}{lll} \displaystyle{\log_{2}(M)=3'5} & \hbox{y} & \displaystyle{\log_{2}(N)=-1'4,} & \hbox{determina:}\\ \end{array}\right. \)

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

Actividad (#3)

Expresa como un solo logaritmo:

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

Actividad (#4)

Determina la relación que existe entre \(x\) e \(y\) para que se cumpla:

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

Actividad (#5)

Si consideramos que \( \left.\begin{array}{lll} \displaystyle{\log_{}(3)=0'477} & \hbox{y} & \displaystyle{\log_{}(2)=0'301,} & \hbox{determina:}\\ \end{array}\right. \)

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