Use this information to evaluate the following. Hint: do not try to solve for the value of a. loga 2 = 0.32
loga 3 = 0.50
loga 5 = 0.73

a. loga 15 =
b. loga (5/3) =
c. loga(8a7)

a. 1.23

b. 0.23

c. 7.96

Step-by-step explanation:

Use laws of logarithms:

log(a*b) = log(a) + log(b)

log(a/b) = log(a) - log(b)

log(a^b) = b*log(a)

log_k(k) = 1

a. log_a(15) = log_a(3*5) = log_a(3) + log_a(5) = 0.50 + 0.73 = 1.23

b. log_a(5/3) = log_a(5) - log_a(3) = 0.73 - 0.50 = 0.23

c. log_a(8*a^7) = log_a(8) + log_a(a^7) = log_a(2^3) + log_a(a^7)

  = 3log_a(2) + 7log_a(a) = 3(0.32) + 7(1) = 7.96