Question

Sendo Log de base 2 (5) = M, Calcule em funçao de M os seguintes logaritmos:
a) Log base 4 (25)
b) Log de base 8 (√5)
c) Log de base 5^100 (2^100)

Answer 1

$Log_25 = m \\ \\ \\ a) \\ log_425= \dfrac{log_225}{log_24} =\dfrac{log_25^2}{log_22^2}=\dfrac{2log_25}{2log_22}=\dfrac{2m}{2.1}=m \\ \\ \\ \\ b) \\ log_8 \sqrt{5} =\dfrac{log_2\sqrt{5}}{log_28}=\dfrac{log_25^{\frac{1}{2}}}{log_22^3}=\dfrac{\frac{log_25}2}{3log_2.2}=\dfrac{\frac{m}2}{3.1}=\dfrac{m}{2}.\dfrac{1}{3}=\dfrac{m}{6} \\ \\ \\ \\ c) \\ log_{5^{100}}2^{100}= \dfrac{log_22^{100}}{log_25^{100}} = \dfrac{100log_22}{100log_25} =\dfrac{log_22}{log_25} = \dfrac{1}{m}$

=)