Question

Determine o logaritmo:

Answer 1

Resposta:

a) $\frac{5}{2}$

b) $\frac{2}{3}$

c) $-\frac{3}{2}$

d) $\frac{3}{4}$

Explicação passo a passo:

a) $\log _4\left(32\right)=\log _{2^2}\left(32\right)=\frac{1}{2}\log _2\left(32\right)=\frac{1}{2}\log _2\left(2^5\right)=\frac{1}{2}\cdot \:5=\frac{5}{2}$

b) $\log _{27}\left(9\right)=\log _{3^3}\left(9\right)=\frac{1}{3}\log _3\left(9\right)=\frac{1}{3}\log _3\left(3^2\right)=\frac{1}{3}\cdot \:2=\frac{2}{3}$

c) $\log _4\left(\frac{1}{8}\right)=\log _{2^2}\left(\frac{1}{8}\right)=\frac{1}{2}\log _2\left(\frac{1}{8}\right)=\frac{1}{2}\log _2\left(2^{-3}\right)=\frac{1}{2}\left(-3\right)=-\frac{3}{2}$

d) $\log _4\left(\sqrt{8}\right)=\log _{2^2}\left(\sqrt{8}\right)=\frac{1}{2}\log _2\left(\sqrt{8}\right)=\frac{1}{2}\log _2\left(2^{\frac{3}{2}}\right)=\frac{1}{2}\cdot \frac{3}{2}=\frac{3}{4}$