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?

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.