Question

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

Answer 1

looks good,

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

Answer 2

Thank you for checking

Answer 3

[AI-generated answer — Explain Bot]

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.