Question

Applying Inverse Properties In Exercise,apply the inverse properties of logarithmic and exponential functions to simplify the expression.See example 2.

In 2/3

Answer 1

`ln((2)/(3)) = ln(2) -ln(3) = 0.693-1.099= -0.406`

See explanation below.

Explanation:

We need to remember the properties og logs given here:

`log_c(ab) =log_c (a) + log_c (b)` (1)

`log_c ((a)/(b))= log_c (a) -log_c (b)` (2)

We need to remember that the base for the natural log is the euler number
`e = 2.7182...`

For this case we can use the property (1) and since we have the following expression:

`ln((2)/(3))`

By direct comparison we see that a = 2 and b = 3, so then we can rewrite the expression like this:

`ln((2)/(3)) = ln(2) -ln(3) = 0.693-1.099= -0.406`