10Log 1000 + 100 Log 1000 + 1000 Log 1000 =

We can solve this step by step. The logarithmic expression given is:

\[
10 \log 1000 + 100 \log 1000 + 1000 \log 1000
\]

### Step 1: Simplify \(\log 1000\)
Since \(1000 = 10^3\), we can use the logarithmic property \(\log 10^a = a\log 10\) and \(\log 10 = 1\):

\[
\log 1000 = \log 10^3 = 3
\]

### Step 2: Substitute \(\log 1000 = 3\) into the expression

\[
10 \log 1000 + 100 \log 1000 + 1000 \log 1000 = 10(3) + 100(3) + 1000(3)
\]

### Step 3: Perform the multiplications

\[
= 30 + 300 + 3000
\]

### Step 4: Add the terms

\[
30 + 300 + 3000 = 3330
\]

### Final Answer:

\[
10 \log 1000 + 100 \log 1000 + 1000 \log 1000 = 3330
\]

Would you like any further details or have any questions?

Here are some related questions:
1. How do you calculate logarithms for numbers other than powers of 10?
2. What are the main properties of logarithms used in simplifying expressions?
3. How does the change of base formula work in logarithms?
4. Can logarithms be used to solve exponential equations? How?
5. How do logarithmic scales relate to real-world applications like sound intensity?

**Tip:** Remember that logarithms are the inverse of exponentiation and are especially helpful in dealing with very large or very small numbers!

10 Log 1000 + 100 Log 1000 + 1000 Log 1000 =

Discover how to solve the logarithmic expression 10 Log 1000 + 100 Log 1000 + 1000 Log 1000 step by step. This problem involves key logarithmic concepts and properties, making it suitable for students in Grades 9-12. Learn the logarithmic rules for simplifying powers of 10.

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