Propeties of logarithms

Question

If logb3 = 0.5 and logb5 = 0.7, evaluate each expression.

1.) Logb 5/3

Answer 1

One of the properties of logarithms is that log_b(m/n) = log_b(m) - log_b(n)

Applying this property to log_b(5/3) means log_b(5/3) = log_b(5) - log_b(3)

Substituting that log_b(3) = 0.5 and log_b(5) = 0.7 we get log_b(5/3) = 0.7 - 0.5 therefore log_b(5/3) = 0.2

Answer 2

Hello Kat.

You want to use the quotient rule for logarithms:

log_b 5/3 = log_b5 - log_b3 = 0.7 - 0.5 = 0.2

log_b 5/3 = 0.2