If log 27 = 1.431, then the value of log 9 is:



a.
0.934

b.
0.945 

c.
0.958

d.
0.954 

We are given that:

\[
\log 27 = 1.431
\]

Our task is to find the value of \(\log 9\).

First, express both 27 and 9 in terms of powers of 3:
\[
27 = 3^3 \quad \text{and} \quad 9 = 3^2
\]

Using the logarithmic identity:
\[
\log(a^b) = b \cdot \log a
\]

We can express \(\log 27\) and \(\log 9\) as follows:
\[
\log 27 = \log(3^3) = 3 \cdot \log 3
\]
\[
\log 9 = \log(3^2) = 2 \cdot \log 3
\]

From \(\log 27 = 1.431\), we know:
\[
3 \cdot \log 3 = 1.431
\]

Solving for \(\log 3\):
\[
\log 3 = \frac{1.431}{3} = 0.477
\]

Now, substitute \(\log 3\) into the expression for \(\log 9\):
\[
\log 9 = 2 \cdot \log 3 = 2 \cdot 0.477 = 0.954
\]

Thus, the value of \(\log 9\) is:

\[
\boxed{0.954}
\]

### Answer: d. 0.954

Do you have any questions or want more details on the steps? 

Here are 5 questions to further explore logarithms:
1. What is the logarithmic property that relates the logarithm of a product to individual logarithms?
2. How would you find \(\log 81\) if you know \(\log 27\)?
3. What is the change of base formula for logarithms, and how is it used?
4. How does the value of \(\log 9\) change if the base is 2 instead of 10?
5. Can you explain why logarithms are useful in solving exponential equations?

**Tip:** When working with logarithms, always try to express the numbers in terms of powers of the same base for simpler calculations.

If log 27 = 1.431, then the value of log 9 is:
a. 0.934
b. 0.945
c. 0.958
d. 0.954

Learn how to solve for log 9 using logarithmic identities given that log 27 = 1.431. This step-by-step solution explains how to apply the log power rule and basic logarithmic concepts. Suitable for students in Grades 10-12.

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