Question

Write the expression as a single natural logarithm. 2 ln 8 + 2 ln y

Answer 1

2 ln 8 + 2 ln y

The first thing we could do is use the distributive property and "take out" the 2.

After we do that, we get

2( ln 8 + ln y)

Here's a cool property of logarithms of any base.

log a + log b = log ab

Note: The bases of the logarithms must be the same for this to work.

Let's apply that property

2 (ln 8 + ln y)
= 2 ln 8y

That could be your answer. If you want to remove the 2, we can use the following property:

a log b = log (a^b)

2 ln (8y)
= ln (8y)^2
= ln (64y^2)

That could be another answer.

Have an awesome day! :)