Given that $\log_{10} 3 = 0.4771$, we are tasked with finding the value of $\log_{10} 81$.

First, recognize that 81 is a power of 3: $81 = 3^4$

Using the logarithmic property $\log_b(x^n) = n \log_b x$, we can write: $\log_{10} 81 = \log_{10} (3^4) = 4 \log_{10} 3$

Substituting the given value of $\log_{10} 3 = 0.4771$: $\log_{10} 81 = 4 \times 0.4771 = 1.9084$

Now, comparing the calculated value to the options:

• (a) 0.7
• (b) 0.9
• (c) 1.1
• (d) 1.3

None of the provided answers match directly, but since $1.9084$ rounds to approximately 1.9, this suggests that the answer might have been truncated or rounded incorrectly.

Thus, none of the given options seem to be correct based on this calculation.

Would you like more details on logarithmic properties, or do you have further questions?

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Here are 5 related questions:

1. What is the value of $\log_{10} (3^5)$?
2. How would you solve $\log_{10} 243$ given $\log_{10} 3 = 0.4771$?
3. Can you find the value of $\log_{10} 9$ using properties of logarithms?
4. What are the general properties of logarithms and how do they apply in simplifications?
5. How do you calculate logarithms for large powers of numbers like $\log_{10} 10000$?

Tip: When solving logarithmic problems, always look for powers of known numbers to simplify calculations.