Question

Evaluate each logarithm using properties of logarithms and the following facts. logₐ (x)=3.9logₐ (y)=1.4logₐ (z)=2.1 (a) logₐ (yz)

Answer 1

To find log_a(yz), we use the logarithm property that states the log of a product equals the sum of the logs. Given log_a(y) = 1.4 and log_a(z) = 2.1, we add the two to get log_a(yz) = 3.5.

Step-by-step explanation:

We are asked to evaluate loga (yz) using the given logarithmic values:

• loga (x) = 3.9
• loga (y) = 1.4
• loga (z) = 2.1

Using the property of logarithms:

1. The logarithm of a product of two numbers is the sum of the logarithms of the two numbers.

We can find the value of loga (yz) as follows:

loga (yz) = loga (y) + loga (z)

Substituting the given values:

loga (yz) = 1.4 + 2.1

loga (yz) = 3.5