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To solve the given logarithmic equation:

\[
\log(x + 9) = \log(x) + \log(9)
\]

We can apply logarithmic properties to simplify and solve for \(x\).

### Step 1: Use the logarithmic property \( \log(a) + \log(b) = \log(ab) \).
The right-hand side of the equation becomes:
\[
\log(x + 9) = \log(x \cdot 9)
\]

### Step 2: Since the logs on both sides are equal, we can drop the logarithms and equate the arguments:
\[
x + 9 = 9x
\]

### Step 3: Solve the equation for \(x\).
\[
x + 9 = 9x
\]
Subtract \(x\) from both sides:
\[
9 = 8x
\]
Now, divide both sides by 8:
\[
x = \frac{9}{8} = 1.125
\]

### Step 4: Verify if the solution is valid.
We must check that \(x = 1.125\) is within the domain of the original logarithmic expressions. Since the arguments of the logarithms must be positive, \(x > 0\), and \(x = 1.125\) satisfies this condition.

Thus, the solution to the equation is:

\[
x = 1.1250
\]

Would you like more details, or do you have any further questions?

Here are five related questions:
1. What are the common logarithmic properties used in equation solving?
2. How would the solution change if the equation involved natural logarithms (\(\ln\)) instead?
3. What happens if the argument of a logarithm is negative or zero?
4. Can logarithmic equations have more than one solution? Why or why not?
5. How can you graphically interpret the solution to a logarithmic equation?

**Tip**: When solving logarithmic equations, always check the domain of the logarithmic function to ensure that the argument remains positive.

Solve the following logarithmic equation: log(x + 9) = log(x) + log(9). Round your answer to 4 decimal places.

Learn how to solve the logarithmic equation log(x + 9) = log(x) + log(9) step-by-step. This problem applies the logarithmic property log(a) + log(b) = log(ab) and covers important algebraic and logarithmic concepts. Suitable for students in Grades 9-11.

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