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The problem given is:

\[
-8 + \log_5(x + 4) = -6
\]

To solve for \( x \), follow these steps:

### Step 1: Isolate the logarithmic term
Add \( 8 \) to both sides to move the constant term:
\[
\log_5(x + 4) = -6 + 8
\]
\[
\log_5(x + 4) = 2
\]

### Step 2: Rewrite the equation in exponential form
The equation \( \log_5(x + 4) = 2 \) can be rewritten using the definition of a logarithm:
\[
x + 4 = 5^2
\]
\[
x + 4 = 25
\]

### Step 3: Solve for \( x \)
Subtract \( 4 \) from both sides:
\[
x = 25 - 4
\]
\[
x = 21
\]

### Answer
\[
x = 21
\]

Would you like further explanation or have any other questions?

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Here are some related questions that might deepen your understanding:
1. What if the base of the logarithm was different, say \( \log_3(x + 4) = 2 \)?
2. How would the solution change if the equation were \( -8 + \log_5(x + 4) = -10 \)?
3. Can you solve \( \log_5(x) = 3 \) using the same principles?
4. How can we solve for \( x \) if the equation were \( \log_5(x + 4) + \log_5(x - 2) = 2 \)?
5. What does the solution \( x = 21 \) represent graphically on a log function plot?

**Tip:** Always remember to check if the argument inside the logarithm is positive when solving for \( x \). This ensures that the solution is valid.

Discover how to solve the logarithmic equation -8 + log₅(x + 4) = -6 with step-by-step guidance. This problem explores key concepts in logarithmic equations, exponential functions, and algebra, suitable for students in Grades 10-12.

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