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

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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:

logb(xn) = n * logb(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.

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