Condense Logarithms Worksheets (printable, online, answers, examples) - Free Printable

Final Answer:
$\log_3 \left( \frac{8}{25} \right)$

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Explanation:
Let’s break this down step by step.

We have:
3 log₃ 2 – 2 log₃ 5

Step 1: Use the “power rule” for logs.
That means:
n × log_b(a) = log_b(aⁿ)

So,
3 log₃ 2 becomes log₃(2³) → which is log₃(8)
2 log₃ 5 becomes log₃(5²) → which is log₃(25)

Now our expression is:
log₃(8) – log₃(25)

Step 2: Use the “quotient rule” for logs.
That means:
log_b(A) – log_b(B) = log_b(A/B)

So,
log₃(8) – log₃(25) becomes log₃(8/25)

And that’s our final answer!

You’re basically turning two separate logs into one neat fraction inside a single log.

✔ Final Answer: log₃(8/25)