loga help please

Question

Given that loga(5)≈0.77and loga(3)≈0.53 , evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the the logarithms of 5 and 3.

a)  loga(125)≈

b)  loga(1.8)≈

c)  loga(√3)≈

d)  loga(75)≈

e)  loga(0.6)≈

f)  loga(15)≈Correct

Answer 1

loga5=.77

loga3=.53

loga125 =loga(5)^3 = 3loga5 = 3(.77) = 2.31

loga1.8 = loga.6 + log3 = loga3 +loga.2 + .loga3 = 1.06 + loga.2 = 1.06 +loga1 -loga5 = 1.06-.77= .29

logasqr3= loga3^.5 = .5loga3 = .5(.53 = .265

loga75 = loga(3(5)(5) = loga3+2loga5 = .53+2(.77) = .53+1.54= 2.07

loga.06= loga(3(.02)) = loga3 + loga.02 = .53 + loga(1/50) = .53 +loga1 - loga50 = .53 +0- log5 -log10

= .53 -.77 - loga10 = -.24 - loga5 - loga2 = -.24-.77 - loga2 = -1.01 - loga2 =-1.454

loga15 = loga(3(5)) = loga3+loga5 = .53+.77 = 1.30