math problem help

Question

Given that loga(4)≈0.63  and  loga(5)≈0.73 , evaluate each of the following. Hint: use the properties of logarithms to rewrite the given logarithm in terms of the the logarithms of 4 and 5.

a)  loga(20)≈

b)  loga(80)≈ 

c)  loga(√5)≈

d)  loga(3.2)≈

e)  loga(0.8)≈

f)  loga(64)≈l

Answer 1

log to base a of 4 = .63

log to base a of 5 = .73

log to base a of 20 = log_a((4)(5)) = log_a4+ log_a5 = .63+.73 = 1.36

loga80 = .63+1.36 = 1.99

loga(sqr5) = .5(.73) = .365

loga3.2= loga4 + loga.8 = .63 - .1 = .53

loga(.8) =loga(8/10) = loga8 -loga10 =loga4 +.5loga4 - loga5- .5loga4= .63-.73 = -.1

loga64= loga(8^2) = 2loga8 =2(loga(4sqr4) =2(loga4+ .5loga4) = 2(.63) + .63 =1.26+.63=1.89