Did I do this correctly?

Use log laws to write the following expression as a single logarithm.
3/2 ln25 + 3 ln2 = ln25 3/2 + ln2^3 = ln125 + ln2^3
=ln125 + ln8
=ln(125*8)
=ln1000

looks good,

always a good idea to check your answer with the original on your calculator.

Thank you for checking

To determine if you have simplified the expression correctly using log laws, let's break down the steps you took:

Step 1: Use the property that ln(a) + ln(b) = ln(a * b).

You correctly applied this property to combine the terms "ln125" and "ln8" into "ln(125 * 8)".

Step 2: Simplify the expression ln(125 * 8).

You correctly simplified the expression "ln(125 * 8)" to "ln1000".

Therefore, based on the steps you provided, it appears that you have simplified the expression correctly.