ln(a² − b²)

ln(a-b) + ln (a+b)

So what is the question?

To simplify ln(a² - b²), we can use a logarithmic identity that states ln(a * b) = ln(a) + ln(b). In this case, we have ln(a² - b²).

Step 1: Factor the expression inside the logarithm.
a² - b² can be factored as (a + b)(a - b).

Step 2: Rewrite ln(a² - b²) using the factored form.
ln(a² - b²) = ln((a + b)(a - b)).

Step 3: Apply the logarithmic identity.
ln((a + b)(a - b)) = ln(a + b) + ln(a - b).

Therefore, ln(a² - b²) simplifies to ln(a + b) + ln(a - b).

The expression ln(a² − b²) represents the natural logarithm of the difference between the squares of a and b. To evaluate this expression, you need to follow a few steps:

Step 1: Factor the expression inside the logarithm.
Rewrite a² − b² as (a + b)(a − b).

Step 2: Take the natural logarithm of the factored expression.
ln((a + b)(a − b))

Step 3: Apply the property of logarithms, which states that the natural logarithm of a product is equal to the sum of the natural logarithms of the individual terms.
ln(a + b) + ln(a − b)

Therefore, the expression ln(a² − b²) simplifies to ln(a + b) + ln(a − b).