Question

Determine o valor numérico de cada uma das expressões. Sabendo que log a= 0,7 b) log b = 0,85 e log c= 0,95

a) log(a. b) b) log( a. b/c) c) log (c/b) d) log (a.b.c) e) log (a/c)
f) log (b/a.c) g) log b na base a
h) log (a. b) na base c

Answer 1

a) $log(a*b) = loga+logb = 0,70+0,85 = 1,55$

b) $log( \dfrac{a*b}{c}) = loga+logb-logc = 0,70+0,85-0,95 = 0,60$

c) $log ( \dfrac{c}{b}) = logc-logb = 0,95-0,85 = 0,10$

d) $log (a*b*c) = loga+logb+logc = 0,70+0,85+0,95 = 2,50$

e) $log( \dfrac{a}{c}) = loga-logc = 0,70-0,95 = -0,25$

f) $log ( \dfrac{b}{a*c}) = logb-loga+logc = 0,85-0,70+0,95 = 1,10$

g) $log_ab = \dfrac{logb}{loga} = \dfrac{0,85}{0,70} = \dfrac{17}{14}$

h) $log_c(a*b) = \dfrac{log(a*b)}{logc} = \dfrac{loga+logb}{logc} = \dfrac{0,70+0,85}{0,95} = \dfrac{1,55}{0,95} = \dfrac{31}{19}$