Loga help please

Question

Given that loga(3)≈0.5and loga(5)≈0.73l, evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the the logarithms of 3 and 5.

a)  loga(1.8)≈

b)  loga(√5)≈

c)  loga(15)≈

 Correct

d)  loga(0.6)≈

e)  loga(75)≈

f)  loga(27)≈

Answer 1

loga(3) = .5

(f) loga27 = loga(3^3) = 3loga3 = 3(.5) = 1.5

log5 = .731

(e) loga125 = loga(5^3) = 3loga5 = 3(.731) = 2.193

(d) loga.6 = loga(3(.2)) = loga3 + loga.2= .5 + loga(1/5) = .5+loga1 - loga5 = .5+0- .731 = -.231

(c) loga15 = loga(3(5)) = loga3 +loga5 = .5+ .731 = 1.231

(b) loga(sqr5) = loga(5^.5) = .5loga5 = .5(.731) = .731/2 = .3655

(a) loga1.8 = loga(9/5) = loga9 - loga5 = loga(3^2)-loga5= 2loga3 -loga5 = 2(.5)-.731 = 1-.731 = .269