How do you evaluate the expression given log₃(a) = 0.631, log₃(a³), and log₃(3)?

To evaluate the expression given the logarithmic values, let’s break this down step by step.

We are provided with the following:

• log₃(a) = 0.631
• log₃(a³)
• log₃(3)

Step 1: Evaluate log₃(3)

Firstly, we know that:

log₃(3) = 1

This is because any logarithm with the same base and the number itself equals 1.

Step 2: Evaluate log₃(a³)

Using the logarithmic identity that states:

log_b(xⁿ) = n * log_b(x)

We can express log₃(a³) as:

log₃(a³) = 3 * log₃(a)

Substituting the value we have for log₃(a):

log₃(a³) = 3 * 0.631

= 1.893

Final Evaluation

So, to summarize:

• log₃(3) = 1
• log₃(a³) = 1.893

This completes your evaluation of the logarithmic expressions provided. If you’d like to compute these further, you could also combine them or use them in subsequent calculations as per your needs.