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The equation presented is:

\[
-8 + \log_2(x + 6) = -5
\]

Let's solve for \( x \):

### Step 1: Isolate the logarithmic term.
Add 8 to both sides of the equation:

\[
\log_2(x + 6) = -5 + 8
\]

Simplifying the right side:

\[
\log_2(x + 6) = 3
\]

### Step 2: Convert the logarithmic equation to an exponential equation.
The equation \( \log_2(x + 6) = 3 \) means:

\[
x + 6 = 2^3
\]

Since \( 2^3 = 8 \):

\[
x + 6 = 8
\]

### Step 3: Solve for \( x \).
Subtract 6 from both sides:

\[
x = 8 - 6
\]

\[
x = 2
\]

Thus, the solution is \( x = 2 \).

Would you like a detailed explanation of any step, or have further questions? Here are 5 related questions:

1. How would the solution change if the logarithm had a different base, like base 10?
2. How can logarithmic properties help in solving more complex equations?
3. What are the general steps for solving logarithmic equations?
4. How do you solve equations where the logarithm is on both sides?
5. How do exponential and logarithmic functions relate graphically?

**Tip:** Always check your solution by substituting it back into the original equation to verify its correctness.

Learn how to solve the equation -8 + log_2(x + 6) = -5. This step-by-step guide demonstrates how to isolate the logarithmic term, convert the logarithmic equation to exponential form, and solve for x. Ideal for students in Grades 9-12 studying logarithmic equations.

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