https://file.aiquickdraw.com/mathbot/file/1725453050007v7lgbnux.jpg

The problem in the image asks for the value of \( x \) when:

\[
x = 2 \log_5 1 + \log_3 81
\]

Let's break it down step by step.

### Step 1: Simplify the expression \( \log_5 1 \)
The logarithm of 1 in any base is 0, so:
\[
\log_5 1 = 0
\]

Thus, the first term becomes:
\[
2 \times \log_5 1 = 2 \times 0 = 0
\]

### Step 2: Simplify \( \log_3 81 \)
We need to express 81 as a power of 3. Since \( 81 = 3^4 \), we have:
\[
\log_3 81 = \log_3 3^4 = 4
\]

### Step 3: Combine the results
The equation now simplifies to:
\[
x = 0 + 4 = 4
\]

Therefore, the value of \( x \) is \( \boxed{4} \).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you evaluate logarithms with different bases?
2. What are the properties of logarithms that are useful in simplifying expressions?
3. How can you convert logarithms to a different base using the change of base formula?
4. What is the significance of logarithms in real-world applications?
5. How would you solve an equation involving a sum of logarithms with different bases?

**Tip:** Remember that the logarithm of 1 is always 0, regardless of the base, because any number raised to the power of 0 equals 1.

What is the value of x when \(x = 2 \log_5 1 + \log_3 81\)?

Learn how to solve the logarithmic equation x = 2log5(1) + log3(81) with a detailed step-by-step solution. This problem explores logarithmic properties and exponentiation, suitable for students in Grades 10-12.

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